0 00:00:02,720 --> 00:00:07,390 Jorge Pullin: Okay. So our speaker today is Chen Chen. We'll speak about entangled mountains and network states. 1 00:00:09,270 --> 00:00:10,260 Qian Chen: Okay. 2 00:00:10,410 --> 00:00:13,690 Qian Chen: sense. For in for introduction. And 3 00:00:14,320 --> 00:00:20,979 Qian Chen: today. I I I would like you today. I would like to talk about entanglement in spin network basis Day 4 00:00:21,480 --> 00:00:35,799 Qian Chen: before I move in detail. I would like to get. So I would like to get you. I would like to get you a briefly introduction to the to loop quantity, and in particular, I will focus on kind of a 5 00:00:36,190 --> 00:00:43,969 Qian Chen: kinematical lubricant gravity which conties general relativity in the style of topological quantum field theory or latest condom field theory. 6 00:00:44,030 --> 00:00:47,159 Qian Chen: The starting point is connection. Try, feel valuable 7 00:00:48,120 --> 00:00:52,040 Qian Chen: in this fundamental in this fundamental bosom work 8 00:00:53,210 --> 00:01:00,310 Qian Chen: in terms of connection, field and the Try field and the by this, by these 2 valuable 9 00:01:03,540 --> 00:01:08,309 Qian Chen: which formalize the general activity in into a constraint system. 10 00:01:08,820 --> 00:01:10,819 Qian Chen: We all the kinematics 11 00:01:10,900 --> 00:01:19,880 Qian Chen: consists of coaching, constraint and spatial divorce and constraint, and, on the other hand, the a very complicated Hamiltonian constraint 12 00:01:20,120 --> 00:01:24,199 Qian Chen: make out the dynamics of the of the loop converty. 13 00:01:24,960 --> 00:01:30,470 Qian Chen: So the wave function of loop on gravity stay is based on some Oriented or in. Take off 14 00:01:32,030 --> 00:01:37,759 Qian Chen: with, as you to Holonomy, with as few hormones as as value as as argument. 15 00:01:38,330 --> 00:01:40,530 Qian Chen: For For instance, in this graph 16 00:01:41,280 --> 00:01:48,059 Qian Chen: each holonomy, which, as you 2 phonomy, tell us how to parallel transport from 1 point to another point. 17 00:01:50,240 --> 00:01:56,129 Qian Chen: and the loop content quantization is realized by heronomy flux algebra. 18 00:02:00,150 --> 00:02:03,620 Qian Chen: which which represent which which which conties the 19 00:02:03,890 --> 00:02:06,929 Qian Chen: fundamental bosom back into a 20 00:02:07,720 --> 00:02:10,610 Qian Chen: quantum commutator. 21 00:02:11,210 --> 00:02:17,060 Qian Chen: and for each for each, as you to for each component of su 2 function. 22 00:02:17,290 --> 00:02:21,249 Qian Chen: we can implement Fourier decomposition. So in this way. 23 00:02:21,860 --> 00:02:25,929 Qian Chen: so in this sense we can identify the 24 00:02:28,950 --> 00:02:33,920 Qian Chen: as the position valuable and the half integer spin 25 00:02:34,060 --> 00:02:37,489 Qian Chen: is identified as the conjugate momentum. 26 00:02:38,120 --> 00:02:47,440 Qian Chen: but in other 2 we still need to made the wave function gauge environment on the local as you to transformation on the local, as you do transformation. 27 00:02:48,480 --> 00:02:58,649 Qian Chen: To do this, we assign in the toilet tensor to each. Vertices. Tell us how to map in going the ingoing tensor state to the outgoing tensor state. 28 00:02:59,580 --> 00:03:08,069 Qian Chen: In this sense, in the toilet among you, recoupling the spin into 0 angle, momentum State entangle this entangle the edge 29 00:03:08,420 --> 00:03:10,540 Qian Chen: in tango at your state, naturally 30 00:03:12,250 --> 00:03:13,940 Qian Chen: and no. So so 31 00:03:14,840 --> 00:03:20,730 Qian Chen: we have a we we use, we we we use our traditional data to label us. 32 00:03:20,840 --> 00:03:25,630 Qian Chen: spin that will basis. They They are graph spin, and in the twin 33 00:03:26,710 --> 00:03:27,800 Qian Chen: so 34 00:03:28,050 --> 00:03:34,320 Qian Chen: wave function of a spin-level basis, state is obtained by growing chronomy, and in the toilet. 35 00:03:35,430 --> 00:03:36,470 Qian Chen: In this way 36 00:03:36,670 --> 00:03:44,989 Qian Chen: a very important, a very crucial property is the females and invariance. Suppose we have supposed we have a spin our state. 37 00:03:45,330 --> 00:04:01,889 Qian Chen: and in this graph, and we can move the graph a little bit on and move the for example, move this, move the edge and the mood of vertices a little bit, and due to the TV more and constraint the 2 spin now State are considering our stage equivalence. 38 00:04:03,980 --> 00:04:06,050 Qian Chen: So 39 00:04:07,320 --> 00:04:15,170 Qian Chen: and now. So. Now this is. This is a very brief introduction for loop kind of gravity, and I should say that loop-controllerity tail a piece 40 00:04:15,640 --> 00:04:23,590 Qian Chen: to a tail piece that forwards, because this is a non perturbative approach which avoid a which avoid diverging. 41 00:04:24,130 --> 00:04:26,330 Qian Chen: and we don't need you before any 42 00:04:26,410 --> 00:04:28,219 Qian Chen: fixed backwards by time. 43 00:04:28,550 --> 00:04:43,089 Qian Chen: So this is a background, independent proposal deal for loop congratulations to a position and quantum fluctuation of spin our business state, which go beyond the semi classical, which can be on semi classical quantity. 44 00:04:44,490 --> 00:04:48,779 Qian Chen: However, we also we also there. There are also some challenges. 45 00:04:49,180 --> 00:04:52,030 Qian Chen: the first. The first challenge is the popping of 46 00:04:52,090 --> 00:04:53,240 Qian Chen: locality. 47 00:04:53,790 --> 00:05:04,660 Qian Chen: Now we, since we can move that we can. We can move the we can move the graph, we can move. We can move the point around. How do we localize the subsystem in the sense of if you more is an imbalance. 48 00:05:05,320 --> 00:05:11,450 Qian Chen: the prescription is to ask the relation of a study which emphasize the relation between subsystem 49 00:05:12,720 --> 00:05:17,970 Qian Chen: and the second challenge is semi-classical limit. Now we are given a content. 50 00:05:18,320 --> 00:05:21,500 Qian Chen: We are given a quantum theory which allow us to 51 00:05:21,740 --> 00:05:25,849 Qian Chen: to have content superposition, superposition, and quantum fluctuation. 52 00:05:25,880 --> 00:05:30,010 Qian Chen: How do we recover classical general relativity from this content theory? 53 00:05:30,170 --> 00:05:39,960 Qian Chen: The prescription is the prescription is to ask the coast screening which kill many quantum fluctuation and quantum superstition. 54 00:05:40,580 --> 00:05:44,800 Qian Chen: The search energy is a long-standing. It's a long-standing pop 55 00:05:45,650 --> 00:05:48,499 Qian Chen: because the hamiltonian constraint is very complicated. 56 00:05:48,870 --> 00:05:52,950 Qian Chen: so the dynamics of lubricon and gravity is super 57 00:05:53,020 --> 00:05:54,660 Qian Chen: is a super complicated 58 00:05:55,600 --> 00:05:58,570 Qian Chen: to outcome. To overcome this complexity. 59 00:05:59,310 --> 00:06:12,340 Qian Chen: a possible way, way out is to to look at holography because the Council way charge of a deep, dimensional gravitational system can be defined on a D minus one dimensional boundary. 60 00:06:13,690 --> 00:06:20,269 Qian Chen: And now I've I follow, I I I follow. I follow this challenge and prescriptions. 61 00:06:21,000 --> 00:06:26,659 Qian Chen: I I should say that the quantum in quantum information theory become relevant for the Loop Chronic gravity. 62 00:06:26,990 --> 00:06:36,849 Qian Chen: because we don't have any. We don't have any background, geometry, so the quantum geometry of quantum gravity should be reconstructed from quantum information. 63 00:06:38,000 --> 00:06:39,590 Qian Chen: Indeed, in 64 00:06:40,620 --> 00:06:44,710 Qian Chen: as the least as this list as this. This, this this 65 00:06:44,990 --> 00:06:53,059 Qian Chen: we have a we study, we have, we have, we have, we have, we have studied the to model for Black Hole and the information parallel. 66 00:06:53,130 --> 00:06:59,360 Qian Chen: and also we. We are going to have area law and war in law in some cases, and 67 00:06:59,620 --> 00:07:15,020 Qian Chen: and and and and when we, when we come to, when we comes to who are open content system we have with the coherence, and because they see, because in our state it's the most, many body system we also have for. 68 00:07:15,210 --> 00:07:18,299 Qian Chen: tens of tens of network prosperity. 69 00:07:19,170 --> 00:07:23,099 Qian Chen: and also to be called typicality. And 70 00:07:23,150 --> 00:07:25,030 Qian Chen: some more time. 71 00:07:25,210 --> 00:07:40,010 Qian Chen: And nevertheless we will move. We will, we will go to a conference to consider the relation between the suburbs subsystem and and very interesting. We we have some content simulation for content 72 00:07:40,470 --> 00:07:44,530 Qian Chen: gravity, and which can be implemented in a laboratory. 73 00:07:45,820 --> 00:07:53,909 Qian Chen: And now I I I want to. I want to pay attention to the area law because this has something to do with holography. 74 00:07:54,890 --> 00:08:04,680 Qian Chen: and it's very likely to have to have quantities dynamics holographically, because, as we know, that Black Black Hole entropy 75 00:08:04,740 --> 00:08:09,169 Qian Chen: is proportional to the area of her horizon, and the second. 76 00:08:09,390 --> 00:08:10,669 Qian Chen: and secondly. 77 00:08:11,500 --> 00:08:20,490 Qian Chen: the costly local councilway charge, for example, across the local energy is defined. It can be confused on a twod surface. 78 00:08:20,670 --> 00:08:33,520 Qian Chen: so I I prefer we, for I I prefer to refer holography principle as in this way the gravitation of the we've done in the 2D manifold can be in code in the 79 00:08:33,710 --> 00:08:35,919 Qian Chen: D minus one dimensional boundary. 80 00:08:36,080 --> 00:08:40,639 Qian Chen: But in this talk I don't I don't have enough 81 00:08:40,679 --> 00:08:49,139 Qian Chen: to to to to talk about the dynamics, but I will pull the boundary bulk bungy relation into emphasize. 82 00:08:50,520 --> 00:08:52,000 Qian Chen: and 83 00:08:53,050 --> 00:09:04,670 Qian Chen: and also I will pay attention to the to the entanglement. This is the unffactorized ability of Condon State, which tell us there is that to a correlation 84 00:09:05,130 --> 00:09:13,330 Qian Chen: that can be interpreted classically, so a composite content state will carry much more information than a local state. 85 00:09:14,350 --> 00:09:21,969 Qian Chen: And now we are going to. We are going to have some additionally between content geometry and correlation, since we want to construct a 86 00:09:22,060 --> 00:09:40,720 Qian Chen: quantum geometry from content information. So we have a some. We have now the distance in some time model, and we have. We also now the miti, which is, is, is express in terms of the correlation function of flux operator. And what part of the curvature and this is this is the 87 00:09:40,730 --> 00:09:43,569 Qian Chen: go. This is one of the go of this talk. 88 00:09:44,140 --> 00:09:50,070 Qian Chen: so I will also outline all right the the goal of this talk to study the entanglement 89 00:09:50,100 --> 00:09:52,010 Qian Chen: in spin that was state 90 00:09:52,250 --> 00:09:54,080 Qian Chen: in particular, the many. 91 00:09:54,180 --> 00:09:56,289 Qian Chen: many partly entangled, measure the 92 00:09:56,310 --> 00:10:00,680 Qian Chen: to quantify how much entangle, how how much entanglement 93 00:10:00,900 --> 00:10:03,130 Qian Chen: the spin that will stay carried. 94 00:10:04,130 --> 00:10:13,449 Qian Chen: and also we try. I I also. I try to reconstruct it the curvature from the notion of quantum entanglement and correlation. 95 00:10:14,550 --> 00:10:16,539 Qian Chen: and I will, I will. 96 00:10:17,440 --> 00:10:19,120 Qian Chen: and I will also 97 00:10:19,180 --> 00:10:25,419 Qian Chen: to see how the bulk boundary relation may sense in the contest of entanglement. 98 00:10:26,300 --> 00:10:36,269 Qian Chen: So this is the this is the part of introduction. Oh, do we? if if you have any question, please. please, don't hesitate to interrupt me. 99 00:10:36,610 --> 00:10:43,800 Abhay Vasant Ashtekar: Okay, so can I drop this? I I I was very sympathetic with everything you said except for this holography. 100 00:10:44,020 --> 00:10:52,100 Abhay Vasant Ashtekar: I don't see any evidence for this holography. I mean the Black Hole entropy calculation. Yes, I mean there's a the degrees of freedom 101 00:10:52,200 --> 00:10:52,950 Abhay Vasant Ashtekar: all right. 102 00:10:52,970 --> 00:10:54,340 Abhay Vasant Ashtekar: We can code it in the 103 00:10:54,670 --> 00:10:56,630 Abhay Vasant Ashtekar: quantum geometry of the horizon. 104 00:10:56,920 --> 00:11:00,000 Abhay Vasant Ashtekar: but if I look at the Hamiltonian constraint 105 00:11:00,230 --> 00:11:04,470 Abhay Vasant Ashtekar: that was. 106 00:11:04,530 --> 00:11:05,510 Abhay Vasant Ashtekar: or even 107 00:11:05,570 --> 00:11:06,570 Abhay Vasant Ashtekar: the 108 00:11:07,410 --> 00:11:09,600 Abhay Vasant Ashtekar: the the 109 00:11:09,730 --> 00:11:11,419 Abhay Vasant Ashtekar: there is no 110 00:11:11,450 --> 00:11:19,410 Abhay Vasant Ashtekar: reduction right in the sense of it that I got a graph, and then I just look at the boundary. I I had to look at the entire graph 111 00:11:19,780 --> 00:11:25,790 Abhay Vasant Ashtekar: which is so. I don't see any sense in which holography is realized in new point of gravity 112 00:11:25,900 --> 00:11:27,390 Abhay Vasant Ashtekar: in the 113 00:11:27,800 --> 00:11:32,969 Abhay Vasant Ashtekar: the dynamical sector. So perhaps you can explain what you meant. 114 00:11:33,770 --> 00:11:35,100 Qian Chen: I mean. 115 00:11:35,160 --> 00:11:39,469 Qian Chen: Yeah, I actually I don't. I I I don't have a I don't have a very confident 116 00:11:39,950 --> 00:11:56,049 Qian Chen: I don't have a very confident answer to to to your question. Basically I mean, if we because if we we back to the 3D gravity, pure gravity, and the all the degree of freedom are carried by the bungee. So in this sense we say that the series holiday. And of course. 117 00:11:56,220 --> 00:12:03,110 Abhay Vasant Ashtekar: if we move to the to a 40, that's not true. You look kind of gravity right? I mean, either in classical theory, or in Conduit theory 118 00:12:03,350 --> 00:12:07,180 Abhay Vasant Ashtekar: that the degrees of freedom are all. All of them are in the boundary. 119 00:12:07,250 --> 00:12:10,379 Abhay Vasant Ashtekar: It maybe, or you need something that I Don't understand 120 00:12:10,550 --> 00:12:21,979 Abhay Vasant Ashtekar: we're not. As I was just saying, the Hamiltonian framework who don't see this that the degrees of freedom out of the boundary the Hamiltonian constrained by teama and mud or other I and so on. 121 00:12:22,190 --> 00:12:31,709 Abhay Vasant Ashtekar: and it's in forms. Also, I got the whole graph. I don't look at, so to say, it just the boundary of that graph and that evolution, on the whole, graph, not just the boundary of that. 122 00:12:35,310 --> 00:12:42,709 Qian Chen: Yeah, I actually I don't see. I I. I don't see any holography in the in the team and Hamiltonian, but I am. Why, I want to say, is that 123 00:12:43,660 --> 00:12:53,569 Qian Chen: is it possible to to phone lines to formalize the general relativity into a holography way, and which me that you can find all the dynamical console way, charge. 124 00:12:53,910 --> 00:13:00,600 Qian Chen: defy on the boundary so, and and then I try to. I I try to represent those cons of a charge. 125 00:13:00,780 --> 00:13:04,999 Qian Chen: Those boundary comes away. Charge as the starting point for the quantization. 126 00:13:06,170 --> 00:13:14,310 Abhay Vasant Ashtekar: all right. So this is a program. I mean, it's not that this is what it's realized it. Look on them gradually. You're saying that something like this will happen. Okay, Thank you. 127 00:13:14,740 --> 00:13:16,989 Qian Chen: Okay, okay, Thank you. Thank you for the question. 128 00:13:17,760 --> 00:13:23,950 Qian Chen: And now I so I I try to bet you the I try to buy to the entanglement and try to buy to the entanglement. 129 00:13:24,990 --> 00:13:31,400 Qian Chen: But so the second part is about the coverage for the relation between curvature and the multipartite entanglement. 130 00:13:32,160 --> 00:13:34,719 Qian Chen: But before but before moving into 131 00:13:35,110 --> 00:13:40,050 Qian Chen: into detail, let's look at, let's look at a very simple, a very simple cases. 132 00:13:40,720 --> 00:13:53,439 Qian Chen: So I would like to in this 2 slide I I would like to distinguish the 2 notion of entanglement in the twin entanglement and the bungee entanglement in the toilet entanglement is the entanglement between the 2 vertices 133 00:13:53,610 --> 00:13:54,910 Qian Chen: between 2, 134 00:13:55,880 --> 00:14:00,099 Qian Chen: and the bounty entanglement is the entanglement between the boundary state. 135 00:14:00,560 --> 00:14:07,859 Qian Chen: so you can see that they refactorize the hib the spay in this way, and then we study the entanglement and the bounty entanglement. 136 00:14:07,970 --> 00:14:11,660 Qian Chen: But they are different. I need to. I I need to emphasize. They are different 137 00:14:12,120 --> 00:14:12,970 Qian Chen: and 138 00:14:13,060 --> 00:14:29,329 Qian Chen: based on this single, this based on this single link graph, we can see that a spin that would basis stay the in the toyness, the in the entanglement of the spinning. Our basis state will vanish because we don't have any sort of sensible position, or in the toilet collaboration. 139 00:14:29,920 --> 00:14:30,870 Qian Chen: and 140 00:14:31,760 --> 00:14:39,609 Qian Chen: but for the boundary entanglement, the spin network basis state have for non-violent non-vanishing 141 00:14:40,370 --> 00:14:43,539 Qian Chen: spin login contribution. 142 00:14:43,870 --> 00:14:57,890 Qian Chen: and the in the twin and the and the in in Tankerman Doesn't depend on the of polynomial between between. along this edge, because you can see you can do some. You can do some local unitary 143 00:14:58,170 --> 00:15:17,040 Qian Chen: local local as you to get you transformation on this on this vertices, and then you can. You can move the All on to Bungee and this boundary, actually a local, a local unitary transformation for the for this subsystem. So it doesn't it doesn't depend on the 144 00:15:17,110 --> 00:15:19,879 Qian Chen: honomi of folk. 145 00:15:19,960 --> 00:15:35,999 Qian Chen: But this is this is this this conclud conclusion? Only only work for single, this single graph. If we consider we, if we consider some loop structure, this this this holonomic this conclusion for phonomy doesn't help. 146 00:15:36,530 --> 00:15:38,569 Qian Chen: So this is this is 147 00:15:38,950 --> 00:15:42,290 Qian Chen: This is why why I need to do. But I 148 00:15:42,870 --> 00:15:47,280 Qian Chen: But in this part in this talk I will focus on the in the final entanglement 149 00:15:47,320 --> 00:15:53,030 Qian Chen: which, defined by the unfectualizability between the spin network state 150 00:15:53,530 --> 00:15:57,729 Qian Chen: from the perspective of what? Of tensor product of 151 00:15:57,750 --> 00:15:59,350 Qian Chen: what what is state? 152 00:16:02,070 --> 00:16:04,630 Qian Chen: And let's let's get you. 153 00:16:05,040 --> 00:16:12,410 Qian Chen: Let let me let me get you. Let me get you a very simple, very simple cases. So consider a candy graph in this way 154 00:16:12,870 --> 00:16:19,409 Qian Chen: and this can disk, and we we start with the initial. We start with the initial state. 155 00:16:19,710 --> 00:16:22,240 Qian Chen: which is a spin level basis. State 156 00:16:22,440 --> 00:16:29,450 Qian Chen: and this State doesn't carry any in in the total entanglement, because all the spin and in China are fixed. 157 00:16:30,100 --> 00:16:33,519 Qian Chen: And now we can implement a Loop polynomial operator. 158 00:16:33,680 --> 00:16:37,140 Qian Chen: which will introduce some spinsual position 159 00:16:37,300 --> 00:16:38,849 Qian Chen: along the bulk edge. 160 00:16:38,890 --> 00:16:42,089 Qian Chen: So the 2 word is gay entangle. 161 00:16:42,970 --> 00:16:44,610 Qian Chen: And now in this 162 00:16:44,730 --> 00:16:54,350 Qian Chen: and now in this part I will I will focus on. I will focus on the generalization of this picture. I will consider the tree well and spin. I will 163 00:16:54,930 --> 00:16:58,360 Qian Chen: with one topological loop, and in this sense 164 00:16:59,150 --> 00:17:06,119 Qian Chen: the code, the the curvature, your Gary fact in the loop, her nominee operator on this bulk edge. 165 00:17:09,500 --> 00:17:13,999 Qian Chen: And now it's a time to look at the action of Loop Holomi operator. 166 00:17:15,040 --> 00:17:24,259 Qian Chen: The Loop polynomial operator is defined as the classical as a classical as a class function of su 2 representation, and 167 00:17:24,740 --> 00:17:28,260 Qian Chen: along along the edge they are. They are the 168 00:17:29,060 --> 00:17:32,120 Qian Chen: they are the product of we can our dmitry 169 00:17:32,750 --> 00:17:36,699 Qian Chen: and the animal is the spin of the Su. 2 representation 170 00:17:36,840 --> 00:17:39,989 Qian Chen: this operator add on spin that will 171 00:17:40,290 --> 00:17:43,200 Qian Chen: state by by multiplication. 172 00:17:43,310 --> 00:17:45,979 Qian Chen: But I should mention this is a 173 00:17:46,590 --> 00:17:48,210 Qian Chen: for each piece wine 174 00:17:48,290 --> 00:17:52,259 Qian Chen: the we can, our Dimitri will introduce a spin sewer position 175 00:17:52,330 --> 00:17:55,160 Qian Chen: due to the spin, a spin recoupling. 176 00:17:56,340 --> 00:18:06,399 Qian Chen: and this the upb and the lower bound is the is determined by the triangle condition of recover of su 2 recoupling. 177 00:18:07,570 --> 00:18:08,690 Qian Chen: So 178 00:18:09,480 --> 00:18:15,559 Qian Chen: we can, we can, we can. We can represent. We can represent a loopholeonomy operator 179 00:18:16,130 --> 00:18:17,969 Qian Chen: in pencil for a graph. 180 00:18:19,490 --> 00:18:20,260 Qian Chen: and 181 00:18:20,410 --> 00:18:28,280 Qian Chen: it's turned out that the that the representation will will be a product of 60. Simple. 182 00:18:30,090 --> 00:18:39,120 Qian Chen: Because of the trace we will. We will connect it to the open the open edge together, so we will go, and we are going to have some corner. 183 00:18:39,250 --> 00:18:43,420 Qian Chen: and this corner will get us some 6 simple. 184 00:18:43,700 --> 00:18:55,629 Qian Chen: So the transition Mp. 2. So, finally, the transition Mp. 2 is the product is to put that off for 60 symbol and some spin Mp. 2 and a face. In this way. 185 00:18:58,750 --> 00:19:04,990 Qian Chen: moreover, we can we can use. We can use the asymptotical formula for 60 simple. 186 00:19:05,090 --> 00:19:06,809 Qian Chen: and this and 187 00:19:06,860 --> 00:19:14,809 Qian Chen: and when the spin. When spin. When the loop is spin, it's very small compared with other spin. 188 00:19:15,310 --> 00:19:22,240 Qian Chen: In these cases we can write the 60 symbol into this form, and we the d is a we're going to 189 00:19:22,420 --> 00:19:26,660 Qian Chen: It's a small, weak wigan at Dimm tree, determined by the edge. 190 00:19:26,690 --> 00:19:29,329 Qian Chen: By the end of that, by the end of the 191 00:19:29,620 --> 00:19:31,630 Qian Chen: so asymptotically 192 00:19:32,150 --> 00:19:38,990 Qian Chen: the transition Mp. 2 is, it is passed in terms of angle Theta and the spin shifting. 193 00:19:39,240 --> 00:19:40,360 Qian Chen: and the 194 00:19:40,470 --> 00:19:45,580 Qian Chen: which is the product of we can not of small wig, not Dimitri. 195 00:19:47,650 --> 00:19:49,730 Qian Chen: and now it's a 10 back to the 196 00:19:49,960 --> 00:19:53,650 Qian Chen: multiparta entanglement in other 2, in order to 197 00:19:53,880 --> 00:19:59,190 Qian Chen: quantify the entanglement of a spin. Our state. We need to choose the many. 198 00:19:59,600 --> 00:20:02,319 Qian Chen: many, many, many part in tech, I would measure 199 00:20:02,560 --> 00:20:05,040 Qian Chen: and but to remember the oh yeah. 200 00:20:05,650 --> 00:20:09,379 Qian Chen: but remember they are. They are they they they have they 201 00:20:09,590 --> 00:20:15,059 Qian Chen: many, Many better entanglement has to reach a structure than Bipart entanglement. For 202 00:20:16,210 --> 00:20:17,390 Qian Chen: for instance. 203 00:20:17,760 --> 00:20:24,520 Qian Chen: we can't have a Zoom Meeting to decomposition even for the tree part in a trip part entangled state. 204 00:20:24,670 --> 00:20:28,430 Qian Chen: So we don't have this equation anymore. 205 00:20:29,650 --> 00:20:33,659 Qian Chen: and we have for some larger entanglement and no further entanglement. 206 00:20:34,940 --> 00:20:40,159 Qian Chen: For instance, we can. We can write a Ghd state and double state. 207 00:20:40,390 --> 00:20:41,579 Qian Chen: and if we 208 00:20:41,710 --> 00:20:50,079 Qian Chen: we can we can. We can forget the the the, the the circuit will be of G at the State, and the 209 00:20:50,340 --> 00:20:57,740 Qian Chen: and the and the and the rest of to the rest of of bipart in tank. A pipel stay is on entangled. 210 00:20:58,350 --> 00:21:11,669 Qian Chen: but the 4 W's. Day, if we we trace our the silk will be the second, the the first and the second to be, are still entangled. So this is a long to see the meeting of non- factual entanglement. 211 00:21:14,950 --> 00:21:22,530 Qian Chen: And I should say that we have many, there are many. There are many equivalent entanglement measure for many part of entanglement. 212 00:21:22,970 --> 00:21:28,989 Qian Chen: In in this past I allow the geometrical entanglement as the entanglement measure. 213 00:21:30,200 --> 00:21:33,290 Qian Chen: Suppose we have a few steps. 214 00:21:33,530 --> 00:21:37,910 Qian Chen: and the geometrical entanglement is defined by this equation. 215 00:21:38,050 --> 00:21:46,460 Qian Chen: Where the P site is table. The precise taste from all unentangled state. So the geometrical entanglement is defined 216 00:21:46,560 --> 00:21:47,730 Qian Chen: by the mess 217 00:21:47,800 --> 00:21:49,640 Qian Chen: that it might seem more projection 218 00:21:49,850 --> 00:21:51,520 Qian Chen: of 219 00:21:51,920 --> 00:21:54,830 Qian Chen: maximum progression on to the on that 220 00:21:55,070 --> 00:21:58,619 Qian Chen: onto the contents on the site of Content 221 00:21:58,940 --> 00:22:00,709 Qian Chen: on entangled quantum state. 222 00:22:00,850 --> 00:22:15,769 Qian Chen: and the goal of this part is to study the evolution of a geometrical entanglement. Now we we are we initial? We? So we need initial. We so product, state. So we don't have any. We don't have any 223 00:22:16,600 --> 00:22:27,090 Qian Chen: geometrical entanglement. But now we implement some exponential evolution of heronomy operator. So we are going to have a entangled state, and now we 224 00:22:27,190 --> 00:22:32,040 Qian Chen: we are. We are going to look at the evolution of geometrical entanglement we. 225 00:22:33,610 --> 00:22:35,740 Qian Chen: And so 226 00:22:37,070 --> 00:22:40,350 Qian Chen: The My result of of this part is 227 00:22:40,710 --> 00:22:45,099 Qian Chen: is about 3 valent, one-loop spin network. 228 00:22:46,120 --> 00:22:49,090 Qian Chen: and we can compute it. It's my government institution. 229 00:22:49,710 --> 00:22:50,660 Qian Chen: The first. 230 00:22:50,760 --> 00:22:53,919 Qian Chen: the first, derivative with respect to time. 231 00:22:54,150 --> 00:23:01,930 Qian Chen: must be 0; but the second order derivative. Of of geometrical entanglement are equal to the 232 00:23:02,060 --> 00:23:04,660 Qian Chen: dispersion of Holomi operator. 233 00:23:05,700 --> 00:23:07,070 Qian Chen: and we can 234 00:23:07,360 --> 00:23:08,860 Deepak Vaid: question, if I may. 235 00:23:09,670 --> 00:23:12,670 Eugenio Bianchi: I have a question. 236 00:23:12,930 --> 00:23:13,890 Qian Chen: Oh, yeah. 237 00:23:14,430 --> 00:23:20,959 Deepak Vaid: where is the what you're taking a derivative with respect to time, right. So where is the time coming into this picture? 238 00:23:21,330 --> 00:23:26,869 Qian Chen: because the time is the the time coming into the is financial evolution. 239 00:23:26,970 --> 00:23:36,329 Qian Chen: Okay, okay? And and what Hamiltonian are you using? I mean, I I I I I choose the Hamiltonian as the Holonomy operator. 240 00:23:38,090 --> 00:23:38,930 Deepak Vaid: Okay. 241 00:23:39,170 --> 00:23:40,540 Deepak Vaid: All right, thanks. 242 00:23:40,940 --> 00:23:44,559 Abhay Vasant Ashtekar: Okay. Since you had this slide, the the last slide, please. 243 00:23:44,670 --> 00:23:52,020 Abhay Vasant Ashtekar: So you just have this on this slide. Yeah, yeah, this lot. So I just I don't understand symbols. So G stands for? What for the graph or 244 00:23:52,810 --> 00:23:54,910 Qian Chen: what is it? 245 00:23:55,060 --> 00:23:57,849 Qian Chen: Osmotry is me the geological 246 00:23:58,400 --> 00:24:09,150 Abhay Vasant Ashtekar: or geometric Isis, and that so? What is the Major here? The May, I mean you are given a fixed number of vertices. What what is the system? What is the size supposed to be a state 247 00:24:09,560 --> 00:24:12,399 Abhay Vasant Ashtekar: of what I mean on a given graph or on what 248 00:24:13,640 --> 00:24:14,760 Abhay Vasant Ashtekar: fixed. Well. 249 00:24:14,820 --> 00:24:19,539 Qian Chen: it's. It's supposed to be a spin. That will. 250 00:24:19,600 --> 00:24:22,230 Qian Chen: It's it's supposed to be a spin that will stay 251 00:24:23,940 --> 00:24:24,800 up. 252 00:24:24,950 --> 00:24:25,780 Abhay Vasant Ashtekar: Okay. 253 00:24:25,850 --> 00:24:36,899 Abhay Vasant Ashtekar: it's a spin network state. And and can you explain again what 5 was? I just was just too quick. This is a very general. This is a very general 254 00:24:37,110 --> 00:24:38,700 Qian Chen: definition. 255 00:24:39,150 --> 00:24:46,200 Qian Chen: So we want to look at the entanglement. We want to quantify or entanglement of side. And now we choose. 256 00:24:46,250 --> 00:25:04,929 Qian Chen: and and you can, you can separate the hip, the sp of of of of content state into a 2 part. One part is the entangle state, and another part is the on entangled state. And now now the geometrical entanglement is to quantify the distance between the between in t or 257 00:25:04,940 --> 00:25:14,780 Qian Chen: entangled state, to the to the site of an entangled state, so precise is to choose as an arbitrary spin that will stay. 258 00:25:15,330 --> 00:25:18,939 Qian Chen: and the psi is the on entangle spin that will State. 259 00:25:19,300 --> 00:25:29,790 Qian Chen: so the distance will be will be will be measured by the by, the by, the position of a entangled state to a an entangled state. 260 00:25:31,950 --> 00:25:33,560 Abhay Vasant Ashtekar: I I. 261 00:25:34,140 --> 00:25:36,140 Abhay Vasant Ashtekar: Okay. So I 262 00:25:36,800 --> 00:25:41,480 Abhay Vasant Ashtekar: These are not the subspaces of the 263 00:25:42,170 --> 00:25:46,150 Abhay Vasant Ashtekar: We. We just look at. C: yeah, these are not subspaces. They are just 264 00:25:46,310 --> 00:25:48,050 Abhay Vasant Ashtekar: every and and and 265 00:25:48,230 --> 00:25:53,919 Abhay Vasant Ashtekar: you you're wearing on all our unentangled states for a given entangled state. Is that what you're doing here? 266 00:25:55,620 --> 00:25:57,209 Qian Chen: Yes, yes, yes. 267 00:25:57,370 --> 00:26:01,880 Qian Chen: yeah, it's it's no, it's not, it's it's it's No. Because 268 00:26:01,930 --> 00:26:07,660 Qian Chen: if you super, we compose a to 2 or 2 for that day. 269 00:26:07,820 --> 00:26:11,730 Qian Chen: and you will you? You are going to have what you are Mostly you are. 270 00:26:11,880 --> 00:26:15,720 Qian Chen: Most probably you are going to have a entangle. 271 00:26:15,830 --> 00:26:21,639 Abhay Vasant Ashtekar: and and conversely, I can stick. Read your accommodation and titles when I, and tackle State to make them unintended. 272 00:26:21,740 --> 00:26:24,239 Abhay Vasant Ashtekar: So here size is a given 273 00:26:24,640 --> 00:26:27,670 Abhay Vasant Ashtekar: internal state, and 5 are all possible 274 00:26:27,980 --> 00:26:34,680 Abhay Vasant Ashtekar: unentangled states, and you are just looking at this in the product and then taking it. Yeah, yeah, yeah, yeah. 275 00:26:35,540 --> 00:26:36,229 Abhay Vasant Ashtekar: Thank you. 276 00:26:37,080 --> 00:26:54,490 Western: Sorry I have a related question. maybe you said it before, but I may have missed it. So is there any dependence on the graph that you're using to define your state? Or are you considering a a superposition of all possible graph. 277 00:26:54,940 --> 00:26:56,480 Qian Chen: that's pretty I 278 00:26:58,460 --> 00:27:03,889 Qian Chen: in this set. In. In this part I only consider I only consider this kind of 279 00:27:04,090 --> 00:27:05,420 Qian Chen: this kind of graph. 280 00:27:05,500 --> 00:27:17,649 Qian Chen: because for the for the simplicity of computation, but in the last in the in, in the, in the in the next part I will try to generalize to the actual graph. 281 00:27:18,030 --> 00:27:22,849 Qian Chen: So so the conclusion for the for this part I only considered 282 00:27:23,000 --> 00:27:24,410 Qian Chen: this kind of graph. 283 00:27:24,660 --> 00:27:32,229 Qian Chen: but actually this, this definition for entanglement Doesn't: Rely on which graph you choose. 284 00:27:32,270 --> 00:27:44,550 Western: You you mean, just to the first graph or all the graph of the kind or like the okay. Okay, Thank you so much for that. 285 00:27:45,170 --> 00:27:53,080 Qian Chen: Yeah, yeah, I will. I will try to generalize the I will try to generalize the graph in the in the in the nest in the nest part. 286 00:27:53,530 --> 00:27:59,150 Eugenio Bianchi: Can you Can you say also what's the set of subsystems when you say multi-partite? 287 00:27:59,700 --> 00:28:00,490 Qian Chen: Oh. 288 00:28:00,670 --> 00:28:01,890 Qian Chen: it's the 289 00:28:03,970 --> 00:28:17,999 Qian Chen: to stop the system. The subsystem is is decomposed by the by, the vertical state. For example, in this candy graph the subsystem is the what has the in the twin of State. I tends to put that in the twin 290 00:28:18,250 --> 00:28:20,219 Qian Chen: in the twentieth day fee. 291 00:28:20,360 --> 00:28:35,429 Qian Chen: And in this graph in this triangle was the the sub subsystem is the is, the is. The tensor product is that it's a 10 to put out here. Display of a, B and C, and is that for arbitrary 292 00:28:35,550 --> 00:28:37,560 Qian Chen: number of votes. 293 00:28:38,160 --> 00:28:43,699 Qian Chen: So I separated. I separate the subsystem by the with respect to the 294 00:28:43,770 --> 00:28:45,000 Qian Chen: but what is? 295 00:28:47,470 --> 00:28:59,969 Eugenio Bianchi: And the and the question was asked already before I if I can ask again time evolution, you said that you're considered a as a Mytonian, not the with so loop on this single loop that you have here. Is that right? 296 00:29:00,520 --> 00:29:01,730 Qian Chen: yeah. 297 00:29:02,380 --> 00:29:03,360 Eugenio Bianchi: Okay. 298 00:29:05,240 --> 00:29:06,810 Abhay Vasant Ashtekar: this is a mathematical. 299 00:29:06,940 --> 00:29:08,949 Abhay Vasant Ashtekar: and it's not a physical admin. 300 00:29:09,020 --> 00:29:09,749 Abhay Vasant Ashtekar: You: just 301 00:29:11,970 --> 00:29:15,190 Abhay Vasant Ashtekar: yeah, yeah, it's just I mean, you're just saying that 302 00:29:15,510 --> 00:29:19,510 Abhay Vasant Ashtekar: any function or any operator self as an operator can be taken to be 303 00:29:20,420 --> 00:29:21,549 Abhay Vasant Ashtekar: I me, too, again. 304 00:29:21,700 --> 00:29:22,749 Abhay Vasant Ashtekar: and it just 305 00:29:22,780 --> 00:29:24,450 Abhay Vasant Ashtekar: using that it's not the 306 00:29:24,530 --> 00:29:26,380 Abhay Vasant Ashtekar: it is. It is not a physical time. 307 00:29:26,660 --> 00:29:29,900 Qian Chen: Yeah, it's no physical time. It's just a parameter time. 308 00:29:30,160 --> 00:29:30,710 Bye. 309 00:29:31,960 --> 00:29:32,979 Qian Chen: Yeah. Yeah. 310 00:29:37,040 --> 00:29:38,430 Qian Chen: And now. 311 00:29:39,110 --> 00:29:43,060 Qian Chen: in particular. I can bet you the I can bet you the bipart entanglement. 312 00:29:43,100 --> 00:29:47,880 Qian Chen: and then and now we can try to. You can try to compute the linear entropy. 313 00:29:48,110 --> 00:29:53,219 Qian Chen: and we can. We can see that this is the just so twice as the entanglement isitation. 314 00:29:54,010 --> 00:29:55,150 Qian Chen: and in large 315 00:29:55,640 --> 00:30:05,739 Qian Chen: and in particular in large spin limit. We can use the asymptotic formula to be to to rewrite the the geometrical. 316 00:30:06,510 --> 00:30:09,690 Qian Chen: the geometrical entanglement are to the second order 317 00:30:09,910 --> 00:30:10,880 Qian Chen: of time. 318 00:30:11,360 --> 00:30:15,050 Qian Chen: and the pl are the legend Polynomial. 319 00:30:15,110 --> 00:30:16,030 Qian Chen: and this 320 00:30:16,120 --> 00:30:23,240 Qian Chen: firmly. It's very simple in this way, but I only are to the second order probability of time, second order of time. 321 00:30:24,990 --> 00:30:32,349 Qian Chen: And now I try to. I remember all this. We resolved a work from work for 322 00:30:32,810 --> 00:30:38,320 Qian Chen: a tree or tree valve, one loop graph, so I try to 323 00:30:38,470 --> 00:30:40,149 Qian Chen: generalize the picture. 324 00:30:40,700 --> 00:30:43,330 Abhay Vasant Ashtekar: Are you confused about dim dimensions here? 325 00:30:43,400 --> 00:30:47,899 Abhay Vasant Ashtekar: H. Times t has a dimension is dimensionless right? Because you are exponentiating it 326 00:30:48,180 --> 00:30:49,780 Qian Chen: edge 327 00:30:50,140 --> 00:30:54,899 Abhay Vasant Ashtekar: times. T: I mean you are exponential in it. So h times t is dimensionless. 328 00:30:55,280 --> 00:31:07,039 Abhay Vasant Ashtekar: maybe you can. You can. You can. You can divide. You can pay case on h bar over. no, that's not right, whatever it is, but h times t Your framework is dimensionless, but in the next line 329 00:31:07,200 --> 00:31:08,839 Abhay Vasant Ashtekar: you got a superposition 330 00:31:09,910 --> 00:31:11,430 Abhay Vasant Ashtekar: in which 331 00:31:12,660 --> 00:31:14,100 Abhay Vasant Ashtekar: sorry, maybe 332 00:31:15,360 --> 00:31:17,569 Abhay Vasant Ashtekar: maybe next next one or 333 00:31:18,130 --> 00:31:21,460 Abhay Vasant Ashtekar: somewhere. You are a superposition just just just now. Here. 334 00:31:21,940 --> 00:31:27,379 Abhay Vasant Ashtekar: Okay, this is this all fine. But can you? With very showing the next one next transparently just now? 335 00:31:27,820 --> 00:31:29,970 Abhay Vasant Ashtekar: Yeah, in this, in this transparency 336 00:31:30,300 --> 00:31:33,419 Abhay Vasant Ashtekar: you got h squared times t squared, so that is dimensionless. 337 00:31:33,990 --> 00:31:39,729 Abhay Vasant Ashtekar: but the first term has only h square, and so the dimensions don't match. So what's going on here? 338 00:31:44,040 --> 00:31:50,209 Abhay Vasant Ashtekar: previous transformation trans transparency. Everything was matching. But now suddenly you did something that i'm confused about. 339 00:31:51,640 --> 00:31:54,040 Qian Chen: actually, I don't see any 340 00:31:54,280 --> 00:31:58,930 Qian Chen: any. I don't see any, and I don't see any problem by the dimensions 341 00:31:59,080 --> 00:32:03,769 Abhay Vasant Ashtekar: because I Everything has dimensions of it's square. Is that right? Everything is dimension. It's square. 342 00:32:07,080 --> 00:32:13,399 Qian Chen: Yeah. So linear and entropy has dimension of it square. I 343 00:32:13,800 --> 00:32:21,280 Qian Chen: Hmm. I think that's what I I I I I to to to take the 344 00:32:21,760 --> 00:32:29,649 Qian Chen: another distance by the dimension, because you can pay the t as the dimension of a as a dimension of inverse of. 345 00:32:32,220 --> 00:32:34,330 Qian Chen: So in this sense the 346 00:32:34,680 --> 00:32:38,489 Qian Chen: exponential will will be dimensionally. 347 00:32:40,620 --> 00:32:44,219 Abhay Vasant Ashtekar: but it is, it's not Hamiltonian dimension, right? It just a whole lot of money. 348 00:32:44,760 --> 00:32:49,409 Abhay Vasant Ashtekar: so I don't think plan constant helps here at, and t have to be opposite dimensions. 349 00:32:49,430 --> 00:32:52,109 Abhay Vasant Ashtekar: and i'm just confused as to why 350 00:32:52,800 --> 00:32:55,300 Abhay Vasant Ashtekar: and tag of me, and properly as dimensions of it. Square. 351 00:32:55,890 --> 00:32:59,879 Abhay Vasant Ashtekar: I thought it was going to be dimensionless, and I I got confused account. But okay, go ahead. 352 00:33:00,830 --> 00:33:08,660 Deepak Vaid: Okay, okay, I'll see. I'll see is dimensionless. Then it's fine, because in that expression for the entropy. 353 00:33:08,900 --> 00:33:13,440 Abhay Vasant Ashtekar: No, no. I agree that that every term has dimension of it square. 354 00:33:14,040 --> 00:33:17,519 Deepak Vaid: I can see that I I saw a factor of X T. Over Square. 355 00:33:17,870 --> 00:33:19,070 Deepak Vaid: maybe. Yes, I 356 00:33:20,600 --> 00:33:22,769 Deepak Vaid: can. You so that 357 00:33:32,290 --> 00:33:37,009 Abhay Vasant Ashtekar: yeah, okay. So if you say it is, it's square t squared. That is dimensionless. 358 00:33:37,150 --> 00:33:39,570 Abhay Vasant Ashtekar: But the first term has only 8 square. 359 00:33:40,770 --> 00:33:43,110 Deepak Vaid: No, the whole thing is multiplied by t square. 360 00:33:45,010 --> 00:33:46,380 Jorge Pullin: There's a parentheses. 361 00:33:46,860 --> 00:33:52,549 Abhay Vasant Ashtekar: Oh, this oh, I'm: so sorry. I just missed everything. Okay, I I take it all back. 362 00:33:52,590 --> 00:33:53,549 Abhay Vasant Ashtekar: Okay, Thank you. 363 00:33:54,150 --> 00:33:55,550 Qian Chen: Okay, you're welcome. 364 00:33:57,410 --> 00:34:06,799 Eugenio Bianchi: can I? How that formula relates to the one on multi-partite entitlement that you have before in particular what is, say? Not 365 00:34:07,680 --> 00:34:13,940 Eugenio Bianchi: before you had fi inside. And now there's only to say not to. Can you? Can you say how they are related? 366 00:34:14,590 --> 00:34:16,390 Qian Chen: you meet the site. 367 00:34:17,670 --> 00:34:19,360 Qian Chen: you me, the Psi. Here. 368 00:34:19,630 --> 00:34:22,709 Eugenio Bianchi: I understand this is the initial one 369 00:34:22,929 --> 00:34:27,740 Eugenio Bianchi: what I'm asking is, where is the subsystem that's? That's what i'm asking 370 00:34:28,360 --> 00:34:35,520 Qian Chen: the subsystem. The subsystem is the is, the entangled is the in the pointer state at each vertex. 371 00:34:38,969 --> 00:34:44,610 Eugenio Bianchi: Yeah, yeah, one page where you had this way formula. 372 00:34:44,949 --> 00:34:52,000 Eugenio Bianchi: And then you had the linear entropy. I'm asking, Are you using the same definition? what? What? 373 00:34:53,120 --> 00:34:55,120 Eugenio Bianchi: What is the relation between the 2? 374 00:34:56,510 --> 00:34:58,510 Qian Chen: You mean a linear entropy. 375 00:34:58,650 --> 00:35:04,840 Eugenio Bianchi: Yes, for instance, the entropy in this page you have the definition on top. 376 00:35:05,470 --> 00:35:06,740 Eugenio Bianchi: and 377 00:35:07,210 --> 00:35:09,229 Qian Chen: let's pat you the this graph. 378 00:35:09,470 --> 00:35:17,180 Qian Chen: The linear linear entropy is is the is the reduced density matrix of a or B. 379 00:35:18,680 --> 00:35:19,490 Eugenio Bianchi: Okay. 380 00:35:20,160 --> 00:35:26,729 Eugenio Bianchi: So we always reduce into a single node. That's what i'm asking you, always reducing for a single node. 381 00:35:26,970 --> 00:35:32,340 Eugenio Bianchi: or to some of the notes. I just cannot read it in the formula, because that format doesn't 382 00:35:32,470 --> 00:35:35,090 Eugenio Bianchi: say which subsystem it is. 383 00:35:35,570 --> 00:35:39,039 Qian Chen: yet the subsystem is depend on its detail. 384 00:35:39,990 --> 00:35:58,659 Qian Chen: which is determined by the by, the by, the product of who has stay. And and I I I say, I I say the candy graph or or the linear and it's just for this. It's just for this for this, this, this particular cases. But if we move to the triangle graph 385 00:35:58,670 --> 00:36:08,659 Qian Chen: or script you you you will not have, for you will now have the definition of linear of linear entropy, because the because. 386 00:36:10,560 --> 00:36:11,540 Qian Chen: because 387 00:36:11,610 --> 00:36:17,349 Qian Chen: because you you don't have a Schumeter decomposition for the many, many partite entanglement. 388 00:36:17,920 --> 00:36:20,340 Qian Chen: So I I I just say that 389 00:36:20,400 --> 00:36:28,860 Qian Chen: if you back to the better bipartite cases, and the linear entropy is proportional to the, to the 390 00:36:29,260 --> 00:36:31,839 Qian Chen: geometrical entanglement dissertation. 391 00:36:34,110 --> 00:36:34,810 I see. 392 00:36:34,940 --> 00:36:35,689 Okay. 393 00:36:36,290 --> 00:36:37,220 Qian Chen: Okay. 394 00:36:38,480 --> 00:36:39,430 Qian Chen: And 395 00:36:40,570 --> 00:36:55,559 Qian Chen: And now I try to. I try to. I try to generalize the feature, and this this lead us, lead us to the to the entanglement. Co. Co-screen. And in this talk I I refer Co-screen in. So we do that in of. 396 00:36:55,730 --> 00:36:58,010 Qian Chen: of course, of graphic structure. 397 00:36:58,320 --> 00:37:01,860 Qian Chen: For for this illustration you can see that the 398 00:37:02,460 --> 00:37:17,670 Qian Chen: we can we can choose which we can choose to choose a separate, we can choose some subsequent and and we can trace our. We can trace out what the bulk of the normally which defy which define some boundary density matrix. 399 00:37:17,900 --> 00:37:18,910 Qian Chen: Yeah. And 400 00:37:21,240 --> 00:37:23,279 Deepak Vaid: yeah, can I ask a question? 401 00:37:23,500 --> 00:37:24,619 Qian Chen: Yeah, yeah, yeah. 402 00:37:24,770 --> 00:37:28,989 Deepak Vaid: so can you go back to that expression for the geometric entropy. 403 00:37:32,850 --> 00:37:34,399 Qian Chen: you me this equation. 404 00:37:34,670 --> 00:37:36,659 Deepak Vaid: There is the other one where you have a 405 00:37:36,770 --> 00:37:39,279 Qian Chen: maximization over as well. 406 00:37:39,440 --> 00:37:48,399 Deepak Vaid: So so this is this is the so you are maximizing over all of the product States, right? And then 407 00:37:48,490 --> 00:37:51,259 Deepak Vaid: in the next in the next step 408 00:37:53,000 --> 00:38:01,449 Deepak Vaid: you take Si of t. I guess I of t is your State with whose entropy you want to measure right? 409 00:38:03,230 --> 00:38:08,650 Deepak Vaid: and and then what what are the unentangled States with respect to which you are taking that 410 00:38:09,570 --> 00:38:10,700 Deepak Vaid: that projection. 411 00:38:12,480 --> 00:38:16,270 Qian Chen: Yeah, because I choose the initial State as an entangled State. 412 00:38:17,750 --> 00:38:21,609 Deepak Vaid: and that is, that is what is that? That is just the trivalent node 413 00:38:22,350 --> 00:38:31,710 Qian Chen: if you you me, why, the first order? Your question is, that. Does your question me that why the first, all the derivative? Should be 0? 414 00:38:31,890 --> 00:38:36,689 Deepak Vaid: No, I'm. Just asking what are all the and unentangled States with respect to which you are 415 00:38:36,830 --> 00:38:38,779 Deepak Vaid: taking that projection 416 00:38:39,520 --> 00:38:41,809 Qian Chen: part is itself, because 417 00:38:41,860 --> 00:38:46,690 Qian Chen: because when you look at a first-order, derivative 418 00:38:46,730 --> 00:38:52,820 Qian Chen: you just you, you just lead the when you consider the polynomial operator. You just lead a 419 00:38:52,920 --> 00:38:58,210 Qian Chen: lead a spin that will stay a little bit, and then you purchase onto the itself 420 00:38:58,340 --> 00:39:00,810 Qian Chen: onto the onto the initial state. 421 00:39:00,980 --> 00:39:04,720 Deepak Vaid: I see, I see. So the Holonomy operator is an entangling operator. 422 00:39:05,070 --> 00:39:05,799 Qian Chen: Yeah. 423 00:39:07,810 --> 00:39:11,409 Deepak Vaid: you are evolving. You are starting with an unentangled state to begin with. 424 00:39:11,910 --> 00:39:15,909 Qian Chen: Yeah, Good morning with an on entangling operator. 425 00:39:16,470 --> 00:39:17,350 Qian Chen: Yes. 426 00:39:17,540 --> 00:39:19,979 Deepak Vaid: And then you're measuring the 427 00:39:20,090 --> 00:39:24,909 Deepak Vaid: entropy of that evolved state with respect to the initial and 428 00:39:25,700 --> 00:39:26,970 Qian Chen: yes, yes. 429 00:39:27,850 --> 00:39:28,589 Deepak Vaid: okay. 430 00:39:29,510 --> 00:39:32,879 Deepak Vaid: Okay, I I guess that's somewhat the other. Yeah, thanks. 431 00:39:33,210 --> 00:39:34,160 Qian Chen: Okay. 432 00:39:35,440 --> 00:39:37,129 Qian Chen: and no. 433 00:39:37,950 --> 00:39:48,109 Qian Chen: and no. But but but this talk I don't. I I I don't. I don't want to talk about the trade, but by the first co-screen I I I focus on the gauge facing 434 00:39:48,590 --> 00:39:55,020 Qian Chen: which means that we can get this: the polynomial and and have some, and then have some loop is when I walk. 435 00:39:55,640 --> 00:39:56,770 Qian Chen: and this. 436 00:39:57,000 --> 00:40:00,879 Qian Chen: and and then I will. I will look at the evolution of co- 437 00:40:01,600 --> 00:40:05,260 Qian Chen: and study the entanglement between the spin supper network. 438 00:40:05,610 --> 00:40:09,589 Qian Chen: This is the generalization of in the twin entanglement. 439 00:40:11,670 --> 00:40:13,639 Qian Chen: I know. 440 00:40:14,560 --> 00:40:30,080 Qian Chen: and as the as illustration, you can see when we choose a some spin some, some some of the region, or spin up on that, we will nevertheless, to introduce some boundary. So we will. We will study this, we will start the the formulation 441 00:40:30,140 --> 00:40:41,319 Qian Chen: for the for the spin network with boundary, which means that we will study some open spin level, and this picture is is actually motivated by the study of playhole entropy. 442 00:40:41,480 --> 00:40:53,000 Qian Chen: and you can see that in this picture the in this picture the open spinner will have some puncture of a non trivial puncture on the 443 00:40:53,360 --> 00:40:55,829 Qian Chen: on, on the on the twod surface. 444 00:40:57,170 --> 00:40:58,170 Qian Chen: and so 445 00:40:58,250 --> 00:41:05,980 Qian Chen: it's very natural to define it. It's very natural to define a boundary cube display by tensor in those open edge. 446 00:41:07,170 --> 00:41:14,330 Qian Chen: and we can see, and we can consider it the spin network wave function as some bulk boundary map 447 00:41:14,350 --> 00:41:15,600 Qian Chen: in tons of 448 00:41:15,810 --> 00:41:21,189 Qian Chen: holy, allegedly as functional. And then we we are going to have a boundary state. 449 00:41:21,500 --> 00:41:29,410 Qian Chen: and this boundary state is transformed under under the under, under the local as Youtube page transformation. 450 00:41:29,430 --> 00:41:30,330 Qian Chen: So 451 00:41:30,430 --> 00:41:36,879 Qian Chen: when we do where we do the date, a local transformation on the bulk, we will have some boundary hormone. 452 00:41:38,110 --> 00:41:54,739 Qian Chen: Of course we can. We can define a dual boundary here, because this is the this is the this is the boundary state, and this book, the the scalar put out of this dual boundary. Here. The space defined. It's just defined by the scalar part of the spin that will hit the Sp. 453 00:41:56,560 --> 00:42:03,939 Qian Chen: And now remember that this is the boundary state, so we can we, can we? We are going to be a me. 454 00:42:04,120 --> 00:42:14,050 Qian Chen: I mean some decomposition which me that we can decompose. You can decompose a boundary state into some into a total spin, and 455 00:42:14,130 --> 00:42:23,300 Qian Chen: ties some in the twentieth state, and this total spin must be integer because because of the page invariance of spin. Now, State 456 00:42:23,340 --> 00:42:30,899 Qian Chen: and in the twin tell us how to recouple how to recouple countries, boundary spin into this 457 00:42:31,020 --> 00:42:32,270 Qian Chen: total spin. 458 00:42:33,440 --> 00:42:49,970 Qian Chen: and now it's a time to to to to to return to the top of of Co-screen. And this coast screening is done by gauge, facing, which means that we choose for any. For any bulk we choose a. We choose a row, word, test, and choose some mass mode tree. 459 00:42:51,020 --> 00:42:54,809 Qian Chen: But remember, we don't want you. We don't want you from any loop. 460 00:42:56,070 --> 00:43:00,810 Qian Chen: and then we can get. We can implement data transformation, one by one. 461 00:43:01,690 --> 00:43:06,290 Qian Chen: and to to, to, to have to have to have a trivial 462 00:43:06,540 --> 00:43:11,370 Qian Chen: trivial horonom is along along the mass mo tree, and then the 463 00:43:11,670 --> 00:43:15,649 Qian Chen: we can go the boundary. We can go the boundary edge together 464 00:43:16,020 --> 00:43:20,280 Qian Chen: along this maximal tree, because the heronomy now are trivial. 465 00:43:21,370 --> 00:43:30,690 Qian Chen: So we are going to have some loopy spin. I will and the loopy, and the and the loop edge is the edge out of 466 00:43:30,770 --> 00:43:33,940 Qian Chen: at the at the bulk edge out of the maximum tree. 467 00:43:35,200 --> 00:43:41,350 Qian Chen: So we are going to. So we are. We are going to have a have a co-screen in coast green graph. 468 00:43:43,970 --> 00:43:53,279 Qian Chen: So the gauge facing so under the gauge facing under the gauge fee under the gauge facing. We will have. We will have. We can write all 469 00:43:53,310 --> 00:43:55,079 Qian Chen: pong. You stay in this way. 470 00:43:55,170 --> 00:44:00,469 Qian Chen: and we we and and in phone off in form of the 471 00:44:00,540 --> 00:44:01,679 Qian Chen: country state. 472 00:44:01,790 --> 00:44:07,810 Qian Chen: With respect to the co-screen graph, we will have. We will have some boundary chronomy. 473 00:44:08,090 --> 00:44:09,659 Qian Chen: and we can see that 474 00:44:10,390 --> 00:44:22,490 Qian Chen: from the by, the this, this go to physician to serve the scale of product because we can, we can. We can remember we can remember the scanner product of you up on your Hube display. 475 00:44:22,600 --> 00:44:25,739 Qian Chen: So in this sense we are, 476 00:44:25,840 --> 00:44:33,110 Qian Chen: we define. We define a local unitary transformation between between a final graph, and the coastgu in the graph. 477 00:44:35,960 --> 00:44:36,950 Qian Chen: So, because 478 00:44:37,740 --> 00:44:48,730 Qian Chen: due to the due to the definition of entanglement, this is the local unit, a local unitary transformation with respect to the subsequent, so 479 00:44:49,350 --> 00:44:52,049 Qian Chen: the spin and entanglement will no change 480 00:44:52,190 --> 00:44:55,969 Qian Chen: will not change under the under under the cold screening. 481 00:44:57,200 --> 00:44:58,319 Qian Chen: For instance. 482 00:44:58,460 --> 00:45:09,559 Qian Chen: if we want to compute the entanglement between between between the 3 supper region. We only need to look at the code screen, the graph and this 483 00:45:09,980 --> 00:45:11,410 Qian Chen: which me, that the 484 00:45:11,620 --> 00:45:15,740 Qian Chen: entanglement between spin up, and they will equal to this 485 00:45:15,790 --> 00:45:22,370 Qian Chen: equal to the entanglement between those 2 those 3 in the twin 486 00:45:22,930 --> 00:45:24,350 Qian Chen: loopy in the twin. 487 00:45:27,190 --> 00:45:30,759 Qian Chen: And no, we can we? Can. We can. 488 00:45:31,090 --> 00:45:32,059 Qian Chen: Oh, okay. 489 00:45:32,430 --> 00:45:35,679 Deepak Vaid: So there might be more than one maximal tree 490 00:45:35,950 --> 00:45:37,179 Deepak Vaid: for a given grow. 491 00:45:38,830 --> 00:45:44,589 Deepak Vaid: And so you you you you could end up with with inequivalent 492 00:45:44,660 --> 00:45:46,089 Deepak Vaid: for screening right? 493 00:45:46,530 --> 00:45:48,369 Deepak Vaid: Is that is that not a possibility? 494 00:45:49,000 --> 00:45:49,930 Qian Chen: Oh. 495 00:45:50,300 --> 00:45:51,959 Qian Chen: you me that 496 00:45:53,040 --> 00:45:54,550 Qian Chen: this coastguarding 497 00:45:55,060 --> 00:45:58,519 Qian Chen: it's equivalent to other co- screening. 498 00:45:58,650 --> 00:46:00,830 Deepak Vaid: Yeah, I mean that that could be more than one. 499 00:46:01,150 --> 00:46:04,229 Qian Chen: You have an equivalent cost 500 00:46:04,580 --> 00:46:08,570 Qian Chen: it's it's very likely to have an equivalent of squinting 501 00:46:09,660 --> 00:46:23,649 Qian Chen: because it doesn't doesn't, we move any information. But if we you consider to trace our the polynomial email, you will we move some. You will we move some information 502 00:46:25,410 --> 00:46:26,830 Qian Chen: So there 503 00:46:26,920 --> 00:46:31,739 Qian Chen: Basically, they are. Again, it is not necessary to have an equivalent feature. 504 00:46:32,430 --> 00:46:39,320 Deepak Vaid: No; but I mean with with the cancellation of entertainment entropy remain the same for in equivalent course training. 505 00:46:41,090 --> 00:46:48,999 Qian Chen: I know. Sure, I know. Sure, basically I don't see. I I don't see any. I don't see any hints to say that they are equivalent 506 00:46:50,750 --> 00:46:53,109 Deepak Vaid: okay, maybe i'm not. Anyway. 507 00:46:53,150 --> 00:46:54,909 Deepak Vaid: we I can last later. 508 00:46:55,180 --> 00:47:00,999 Qian Chen: yeah, because basically the a another approach. We we are 509 00:47:01,590 --> 00:47:04,860 Qian Chen: another port. You will. We will. We will get us some 510 00:47:04,880 --> 00:47:06,980 Qian Chen: mix or boundary state. 511 00:47:07,200 --> 00:47:08,849 Qian Chen: but the coast screening 512 00:47:09,150 --> 00:47:13,459 Qian Chen: but that co-screening by page fishing doesn't doesn't. 513 00:47:13,830 --> 00:47:16,159 Qian Chen: but but that doesn't get us 514 00:47:16,550 --> 00:47:22,159 Deepak Vaid: what I was saying was 515 00:47:22,550 --> 00:47:23,339 Deepak Vaid: that's 516 00:47:24,220 --> 00:47:26,519 Deepak Vaid: You are choosing a maximum 3 right 517 00:47:27,750 --> 00:47:31,050 Deepak Vaid: and you could have more than one maximum 3 for a given graph. 518 00:47:31,830 --> 00:47:34,130 Qian Chen: Yeah, yeah, of course, of course. 519 00:47:34,320 --> 00:47:36,689 Deepak Vaid: And so if you have more than one maximum 3, 520 00:47:36,830 --> 00:47:41,220 Deepak Vaid: the resulting loopy graphs, the resulting 4 screens with the graphs. 521 00:47:41,710 --> 00:47:47,300 Deepak Vaid: Yeah, yeah, that could be more than one for the same. Starting from the same original crowd. 522 00:47:47,560 --> 00:47:55,429 Qian Chen: Yeah, I will. I will talk about this question. I will ever talk about this question. I will show you that that they are equivalent in the sense of entanglement. 523 00:47:55,870 --> 00:47:56,909 Deepak Vaid: Okay, Great thanks. 524 00:47:57,320 --> 00:48:00,500 Qian Chen: Okay, okay, I will talk about this. This is a good question. 525 00:48:00,630 --> 00:48:01,209 Yeah. 526 00:48:02,120 --> 00:48:12,849 Qian Chen: And now we can. We can. We can. We can make some we can. We can make some gauge we can make some page facing for Holonomy operator, and this one will tell us that 527 00:48:13,360 --> 00:48:17,170 Qian Chen: the the the co-screening of Holonomy operator. 528 00:48:17,270 --> 00:48:36,260 Qian Chen: So let me give you an example so supposed to be so Star is supposed to be start with a squares graph. And now we try to compute the entanglement between the side and the right hand side. And now I I I need to. I need to call screen. I need to call screen 529 00:48:36,530 --> 00:48:42,829 Qian Chen: Co-screen in the the right hand side and the left hand side. And so we are going to have a candy, graph. 530 00:48:42,890 --> 00:48:53,420 Qian Chen: and we can see that the transformation of Holonomy operator, I mean the transition matrix of hlynomial operator is can be written in this way. 531 00:48:53,450 --> 00:48:57,490 Qian Chen: and this W. Present the 532 00:48:57,650 --> 00:49:00,909 Qian Chen: of square Graph and the L presenter 533 00:49:02,580 --> 00:49:04,069 Qian Chen: on this kind of 534 00:49:04,540 --> 00:49:06,540 Qian Chen: So we are going to have for this 535 00:49:07,020 --> 00:49:08,609 Qian Chen: transformation room. 536 00:49:09,500 --> 00:49:11,249 Qian Chen: And so in this way. 537 00:49:12,170 --> 00:49:15,909 Qian Chen: in this in this transformation tell us 538 00:49:15,930 --> 00:49:18,449 Qian Chen: that the evolution will no change. 539 00:49:18,570 --> 00:49:23,399 Qian Chen: so we can study. The spinner will intend to spin level entanglement 540 00:49:24,550 --> 00:49:25,620 Qian Chen: on this 541 00:49:25,640 --> 00:49:28,030 Qian Chen: on this, on this coast screen the graph 542 00:49:29,950 --> 00:49:39,770 Qian Chen: A. As long as as as long as the evolution operator is choose is choosing us. it is choos by the by heronomy operator. 543 00:49:40,510 --> 00:49:41,479 Qian Chen: So 544 00:49:42,940 --> 00:49:51,640 Qian Chen: I will get you. I will get you some. I will get you some conclusion from from from this, from from this, from this from this. 545 00:49:53,480 --> 00:50:03,340 Qian Chen: Let's bet you let's be a let's bet you let's let's bet you the let's bet you the entanglement institution in previous in previous part. 546 00:50:04,000 --> 00:50:09,839 Qian Chen: So in this graph we can gauge fees. We can gauge fees the spin level in this way. 547 00:50:10,080 --> 00:50:12,630 Qian Chen: and now the structure is. 548 00:50:12,810 --> 00:50:16,720 Qian Chen: it's a single. It's a single vertices plus a single loop. 549 00:50:16,740 --> 00:50:27,669 Qian Chen: and we, in order to have for entanglement institution, we only need to compute the expectation of Holonomy and the test, pay 550 00:50:28,050 --> 00:50:30,819 Qian Chen: dispatch the dispassion of her. No. 551 00:50:30,990 --> 00:50:31,859 Qian Chen: So 552 00:50:32,510 --> 00:50:35,399 Qian Chen: in this way we can write down the boundary state. 553 00:50:35,470 --> 00:50:39,799 Qian Chen: We can write down the boundary state, and this is the distribution of total spin. 554 00:50:40,450 --> 00:50:47,569 Qian Chen: and we can. It's very easy to to to. It's very easy to see that the second order derivative 555 00:50:47,780 --> 00:50:49,040 Qian Chen: is, 556 00:50:49,320 --> 00:50:51,749 Qian Chen: is first in this way. 557 00:50:52,670 --> 00:50:53,920 Qian Chen: And now 558 00:50:55,950 --> 00:51:00,209 Qian Chen: a simple example is is to look at a candy graph. 559 00:51:01,270 --> 00:51:02,180 Qian Chen: and this 560 00:51:02,270 --> 00:51:04,159 Qian Chen: this will back to your question. 561 00:51:04,550 --> 00:51:12,270 Qian Chen: and we can we can. We can choose, we can choose 2 different way to gauge fees, the the candy graph we can. We. 562 00:51:12,970 --> 00:51:23,790 Qian Chen: for example, in the first, in the first gauge facing. We choose the we choose K. 2. We choose the edge associated with K. 2 to gauge fees, and now we have some 100 563 00:51:24,240 --> 00:51:33,609 Qian Chen: safe loop with in K one, and we can also gauge the edge associated with K. One. And now we have some 564 00:51:33,720 --> 00:51:38,989 Qian Chen: we have. We have some loop. We have a safe loop with in K 2, 565 00:51:39,160 --> 00:51:42,019 Qian Chen: and now we can see that the 2 566 00:51:42,860 --> 00:51:46,600 Qian Chen: probability distribution are no equal to each other. 567 00:51:46,680 --> 00:51:51,389 Qian Chen: But it's turned out that the entanglement institutions are equal to each other. 568 00:51:51,480 --> 00:51:52,939 Qian Chen: so you can see that 569 00:51:53,080 --> 00:51:55,919 Qian Chen: it always has this has this phone. 570 00:51:56,120 --> 00:51:56,890 Qian Chen: So 571 00:51:57,060 --> 00:52:00,480 Qian Chen: this I I I hope this answer your question. 572 00:52:01,620 --> 00:52:06,120 Qian Chen: So the gauge facing Doesn't so the entanglement 573 00:52:06,240 --> 00:52:09,540 Qian Chen: doesn't we like that doesn't depend on the 574 00:52:09,970 --> 00:52:12,360 Qian Chen: on the on the trice of cage facing. 575 00:52:13,090 --> 00:52:19,140 Qian Chen: And now I I move you, my my, to my my last, my last example. 576 00:52:20,080 --> 00:52:25,179 Qian Chen: So suppose we we we we want to know the entanglement dissertation, or for 577 00:52:25,380 --> 00:52:27,439 Qian Chen: of a and B Z, 578 00:52:28,040 --> 00:52:45,510 Qian Chen: and we have we. We have now. We have a. We have a 2 option to add to atom at the Holonomy operator. One is along this path and another is along this path, and now we can, since we can, since we can get, since we can gauge the we can co-screen them. 579 00:52:45,520 --> 00:52:48,250 Qian Chen: We we hand co-screen in the 580 00:52:50,770 --> 00:52:54,909 Qian Chen: we are going to. We are going to compute the entanglement between the 2 vertices. 581 00:52:55,070 --> 00:53:01,010 Qian Chen: and that the difference the the only difference between the 2 graph is the is the loopy spin. 582 00:53:02,290 --> 00:53:04,170 Qian Chen: and we can. We can see 583 00:53:04,390 --> 00:53:07,450 Qian Chen: that the the entanglement institution 584 00:53:08,070 --> 00:53:09,730 Qian Chen: depend on the past 585 00:53:09,930 --> 00:53:16,779 Qian Chen: is now can convey, is now conveyed to the dependence of spin along the 586 00:53:16,820 --> 00:53:18,510 Qian Chen: or along the safe loop. 587 00:53:20,760 --> 00:53:23,619 Qian Chen: And now, yeah, this is the end of 588 00:53:23,660 --> 00:53:27,479 Abhay Vasant Ashtekar: this is the so in this example, then they did the 589 00:53:28,420 --> 00:53:29,240 Abhay Vasant Ashtekar: yeah. So 590 00:53:29,660 --> 00:53:32,640 Abhay Vasant Ashtekar: the the second derivative of this is, as 591 00:53:33,290 --> 00:53:36,689 Abhay Vasant Ashtekar: will be 7, 9 and 26 about 27, right? 592 00:53:37,390 --> 00:53:43,269 Abhay Vasant Ashtekar: So they are different in the previous example candy graph, they were the same. But here is a different is that the point that you're making on. 593 00:53:43,470 --> 00:53:49,209 Qian Chen: Yeah, yeah, they are different, because you, because you add in on a different path. 594 00:53:51,040 --> 00:53:51,669 Abhay Vasant Ashtekar: Okay. 595 00:53:51,690 --> 00:53:52,870 Abhay Vasant Ashtekar: So it is not. 596 00:53:55,440 --> 00:53:56,930 Abhay Vasant Ashtekar: So. You based on how 597 00:53:57,670 --> 00:53:59,450 Abhay Vasant Ashtekar: it depends how you course. Great is it? 598 00:53:59,640 --> 00:54:01,909 Abhay Vasant Ashtekar: It depends on what it is. 599 00:54:03,050 --> 00:54:09,429 Abhay Vasant Ashtekar: no, I'm still understanding that you front. But yeah, just explain to us the difference between the candy graph and this graph 600 00:54:09,490 --> 00:54:12,570 Abhay Vasant Ashtekar: and the results on what is the same and what is different. 601 00:54:13,510 --> 00:54:27,440 Qian Chen: You mean the candy graph and this one yeah. So this one you explain. You only have one. You only have one loop, so you don't have any try choice to to to choose a a different way to add in on your loop Loop Holonomy operator. 602 00:54:28,370 --> 00:54:36,840 Qian Chen: But you can. What what you can do what, what what you can do on this graph is to choose a different way to gauge fees. 603 00:54:38,590 --> 00:54:40,229 Abhay Vasant Ashtekar: So you have. 604 00:54:40,250 --> 00:54:44,730 Abhay Vasant Ashtekar: So are you saying that this gauge, fixing this can be graph result that you showed us that 605 00:54:44,810 --> 00:54:54,099 Qian Chen: that second day with you doesn't depend on how you gauge fixed right. That's what you just showed us. No, no, no, no, I mean it doesn't it Doesn't. Depend on how? How you gauge fees. 606 00:54:54,520 --> 00:54:57,030 Abhay Vasant Ashtekar: But is that is that result? 607 00:54:57,550 --> 00:55:00,199 Abhay Vasant Ashtekar: Completely, general, or is it only for candy? Gr. 608 00:55:01,550 --> 00:55:02,600 Qian Chen: Oh. 609 00:55:03,530 --> 00:55:08,369 Qian Chen: Yeah, it's it's a very general. It's a very general conclusion 610 00:55:08,870 --> 00:55:12,199 Qian Chen: for for for for for one, for one loop cost. 611 00:55:12,360 --> 00:55:20,680 Qian Chen: But I mean in this graph it's a 2 loop graph because you can do the gauge fees, and you can see that this graph has a 2 loop, one 612 00:55:23,700 --> 00:55:26,839 Qian Chen: and and this will you, I mean. Oh, okay. 613 00:55:27,200 --> 00:55:30,550 Abhay Vasant Ashtekar: So the key differences between one over 2 group, 2 loop clubs 614 00:55:31,110 --> 00:55:32,710 Abhay Vasant Ashtekar: in the one loop graph. 615 00:55:32,890 --> 00:55:35,520 Abhay Vasant Ashtekar: The secondary video did not depend 616 00:55:36,420 --> 00:55:39,120 Abhay Vasant Ashtekar: on how you gauge fixed. And here 617 00:55:39,300 --> 00:55:42,989 Abhay Vasant Ashtekar: the second derivative in the 2 methods that you showed us up here 618 00:55:43,110 --> 00:55:45,579 Abhay Vasant Ashtekar: has a does change. 619 00:55:46,000 --> 00:56:03,540 Qian Chen: No, no, no, I I mean it Doesn't. Depend on how you go to fees to the the spin. That will it's just depend on the on the spin along along the loop, for example, in this, in this graph you choose a. If you choose a pass, you will you. 620 00:56:03,550 --> 00:56:08,989 Qian Chen: you polynomial operator. We are adding on some spin with initial spin, one 621 00:56:09,030 --> 00:56:10,799 Qian Chen: and another. Pass 622 00:56:11,110 --> 00:56:21,779 Qian Chen: your your her. Normally we are adding on initial spin. We've been half so they're different because because because of the the the spin are different. 623 00:56:21,960 --> 00:56:27,139 Qian Chen: but it doesn't matter to the co-screen it doesn't matter to the gauge facing. 624 00:56:30,340 --> 00:56:31,830 Qian Chen: I mean, I mean 625 00:56:32,080 --> 00:56:33,990 Qian Chen: DC. because you 626 00:56:34,100 --> 00:56:38,290 Qian Chen: if you, if we, if we you are, if you are 627 00:56:38,440 --> 00:56:40,870 Qian Chen: in boundary, you don't know how 628 00:56:41,440 --> 00:56:45,859 Qian Chen: you you don't know which past you you're adding on, but you can 629 00:56:46,020 --> 00:56:50,139 Qian Chen: pass in the past dependency to the spin dependency. 630 00:56:52,670 --> 00:57:00,829 Qian Chen: but actually the the in the to the the entanglement will never, will never depend on the it will never depend on the page facing. 631 00:57:00,880 --> 00:57:03,700 Abhay Vasant Ashtekar: Yes, okay, okay, that's okay. Thank you. 632 00:57:03,990 --> 00:57:06,110 Qian Chen: Okay, okay. Thank you for the question. 633 00:57:06,330 --> 00:57:10,309 Qian Chen: And and and I, I will try to make a conclusion. 634 00:57:11,380 --> 00:57:19,229 Qian Chen: and along this but along this talk I will try to. I will try to present the spin now entanglement 635 00:57:19,320 --> 00:57:24,450 Qian Chen: for the first thing I I do is to define a 636 00:57:24,520 --> 00:57:30,289 Qian Chen: geometrical entanglement are so many, many apartheid entanglement measures for lupoon gravity. 637 00:57:30,340 --> 00:57:39,760 Qian Chen: and the second, I I reconstructed, or find a relation between the second order, entanglement, dissertation to the 638 00:57:39,830 --> 00:57:46,720 Qian Chen: dispersion of loop hormone operator. So in this sense, as we reconstruct it, I reconstructed curvature. 639 00:57:47,340 --> 00:57:50,609 Qian Chen: in terms of entanglement institution. 640 00:57:50,650 --> 00:57:52,689 Qian Chen: This and the so I 641 00:57:53,480 --> 00:58:02,729 Qian Chen: I can. I I show you the spin network entanglement, actually get getting fat in loopy or in loopy in the china. 642 00:58:02,820 --> 00:58:08,299 Qian Chen: and the spin level entanglement is preserved on the page fees on the coast green 643 00:58:08,550 --> 00:58:09,419 Qian Chen: up 644 00:58:11,070 --> 00:58:17,620 Qian Chen: as long as the evolution, as as long as the evolution is generated by the Holonomy operator 645 00:58:18,790 --> 00:58:21,260 Qian Chen: and the and the side 646 00:58:21,360 --> 00:58:35,139 Qian Chen: And the last point, I want to show you that the code screening implied the degree of freedom you have to the spin that will entanglement are in code in the boundary information and the bunk and the bulk, top logic, the top lot. 647 00:58:35,350 --> 00:58:38,780 Qian Chen: the box top top log here is me at the same. 648 00:58:39,270 --> 00:58:41,150 Qian Chen: It's me that a safe loop. 649 00:58:41,370 --> 00:58:51,450 Qian Chen: because you can see that even for for given given folk even you, even you, have a many possible way to to define the co-screen 650 00:58:51,560 --> 00:59:02,439 Qian Chen: you define the page facing you. You are the both. Both top of logic is the is the to my is due to mine by the number, by the relation. 651 00:59:02,980 --> 00:59:09,439 Qian Chen: by the relation of number, or by the by, the relation of number of edge and number of vertices. 652 00:59:10,380 --> 00:59:15,730 Qian Chen: So that's all that's what I want to show. That that's why I want to talk today. 653 00:59:15,940 --> 00:59:17,589 Qian Chen: That's for your attention. 654 00:59:22,530 --> 00:59:23,410 Questions. 655 00:59:34,950 --> 00:59:37,890 Qian Chen: Okay. Hi, John. oh. 656 00:59:38,240 --> 00:59:39,600 Deepak Vaid: no question. 657 00:59:40,820 --> 00:59:44,140 Deepak Vaid: This entanglement operate. sorry. This 658 00:59:44,660 --> 00:59:46,280 Deepak Vaid: phonomy operator. Right? 659 00:59:48,860 --> 00:59:49,879 Deepak Vaid: it it 660 00:59:50,040 --> 00:59:52,419 Deepak Vaid: it is an entangling operator. You said. 661 00:59:53,580 --> 01:00:09,819 Qian Chen: This is a yeah, this is a entangle and operate because it's operator or so many, many many so many vertices, and we will create the spin to a position between the 2 vertices. So you'll create a 662 01:00:10,320 --> 01:00:14,869 Deepak Vaid: and what what is the precise form of this operator. I think I can catch that. 663 01:00:22,090 --> 01:00:24,340 Qian Chen: Here. This is the 664 01:00:24,480 --> 01:00:26,379 Qian Chen: formally for this operator. 665 01:00:26,400 --> 01:00:27,430 Qian Chen: There you are. 666 01:00:28,650 --> 01:00:34,430 Qian Chen: Yet this operate operator is the trade is the trace of Wiganard Dimitri. 667 01:00:36,610 --> 01:00:49,299 Qian Chen: Yeah. And so then to each other. So you will go. You are going to have a Dl. And a G one times 3, 2 times street in, and then you will close the maneuver 668 01:00:49,750 --> 01:00:50,979 Qian Chen: by the sin. 669 01:00:51,550 --> 01:00:54,170 Qian Chen: by the sin. And one so is the choice. 670 01:00:54,660 --> 01:00:55,879 Qian Chen: Oh. 671 01:00:56,060 --> 01:00:57,020 okay. 672 01:00:58,830 --> 01:01:01,270 Deepak Vaid: Oh, okay, I see. So 673 01:01:02,270 --> 01:01:03,520 Deepak Vaid: And okay. 674 01:01:04,940 --> 01:01:05,779 Deepak Vaid: All right. 675 01:01:06,380 --> 01:01:09,450 Deepak Vaid: Can you show me the the the the graph picture. 676 01:01:09,650 --> 01:01:13,520 Qian Chen: the there's a graphical representation like this. 677 01:01:13,650 --> 01:01:14,850 Deepak Vaid: Yeah. 678 01:01:15,550 --> 01:01:16,359 Good. 679 01:01:18,110 --> 01:01:18,779 Okay. 680 01:01:19,650 --> 01:01:22,189 Deepak Vaid: I see. Okay, so 681 01:01:22,310 --> 01:01:24,919 Deepak Vaid: Oh, all right, thanks. Thanks for your 682 01:01:25,390 --> 01:01:26,589 Qian Chen: Oh, you're welcome. 683 01:01:31,020 --> 01:01:33,200 Qian Chen: So basically if you tense 684 01:01:33,260 --> 01:01:35,859 Qian Chen: we cannot demonstrate along this 685 01:01:36,000 --> 01:01:55,659 Qian Chen: along this edge you will have some to open end, and then you are you are. You are summing the Mega negative number. So we connected them to each other, and finally you will connect it all the open end. So we are. You are going to have some corner, and this corner will get you a Secretary. Simple. 686 01:01:59,280 --> 01:02:03,230 Deepak Vaid: right? I I see that now. Yeah, no, thanks. That's very. 687 01:02:04,350 --> 01:02:15,369 Eugenio Bianchi: Can you? Can you see also out the parameter t your time enters? Are you exponentiating this operator? Or are you put in T. As a parameter in a new? 688 01:02:15,450 --> 01:02:19,070 Qian Chen: You? You may need this, this this parameter. 689 01:02:20,350 --> 01:02:21,120 Eugenio Bianchi: Yes. 690 01:02:21,450 --> 01:02:29,339 Qian Chen: Oh, yeah, this is is just a just as up. I say, this is a parameter. This is a just parameter time. 691 01:02:29,920 --> 01:02:36,100 Eugenio Bianchi: Yeah. And the question is, what is age? Is the 692 01:02:36,380 --> 01:02:38,340 Qian Chen: H. Is the whole nomi operator. 693 01:02:39,890 --> 01:02:40,770 Eugenio Bianchi: I see. 694 01:02:41,530 --> 01:02:45,400 Abhay Vasant Ashtekar: So it's that. Use Hamiltonian, and time is really in there 695 01:02:45,640 --> 01:02:49,200 Abhay Vasant Ashtekar: in the general sense, like I mean, given any excel for job Operator. 696 01:02:49,960 --> 01:02:53,350 Abhay Vasant Ashtekar: Yeah. And and the parameter that flow is called 697 01:02:53,460 --> 01:02:56,060 Abhay Vasant Ashtekar: I mean, it's not really the physical. 698 01:02:56,770 --> 01:02:58,390 Qian Chen: Yeah, actually, you can. 699 01:02:58,710 --> 01:03:02,290 Qian Chen: You can place any operator in this formulation. 700 01:03:02,810 --> 01:03:13,120 Abhay Vasant Ashtekar: Yeah, any. It's just to the second chance. So so I mean the the the motivation was a those of us who are not exporting this thing was was a little bit 701 01:03:13,170 --> 01:03:15,190 Abhay Vasant Ashtekar: and clear. So let me just make sure that 702 01:03:17,560 --> 01:03:19,959 Abhay Vasant Ashtekar: that we understand your motivation 703 01:03:19,980 --> 01:03:24,459 Abhay Vasant Ashtekar: of using. I mean, Why, why do you use a lot of me as opposed to anything else? 704 01:03:24,490 --> 01:03:26,240 Abhay Vasant Ashtekar: And is it because you want to 705 01:03:26,420 --> 01:03:28,500 Abhay Vasant Ashtekar: sort of see how curvature 706 01:03:29,130 --> 01:03:31,430 Abhay Vasant Ashtekar: is generating entanglement. 707 01:03:31,450 --> 01:03:32,879 Abhay Vasant Ashtekar: Is that the idea? Or 708 01:03:33,190 --> 01:03:48,150 Qian Chen: yeah, yeah, yeah, basically, yeah, I want to, because I size as I say in the introduction, I want to. I want to see how the I want to see the relation between curvature and the entanglement. So I choose the curvature 709 01:03:49,110 --> 01:03:53,010 Qian Chen: we choose. We choose curvature, or we choose polynomial operator 710 01:03:53,250 --> 01:03:54,549 Qian Chen: to to study. 711 01:03:55,880 --> 01:03:57,470 Qian Chen: And the 712 01:03:58,940 --> 01:03:59,790 Go ahead. 713 01:04:00,290 --> 01:04:01,429 Abhay Vasant Ashtekar: go ahead. And 714 01:04:01,990 --> 01:04:03,430 Qian Chen: yeah, and actually 715 01:04:03,570 --> 01:04:14,820 Qian Chen: actually this yeah, as I as I mentioned and the question, this operator. This operator is the entangling app, which means that you it will create some entanglement. 716 01:04:16,910 --> 01:04:21,319 Abhay Vasant Ashtekar: What is the idea that supposing I give, I mean, I wouldn't understand the physical. I 717 01:04:21,500 --> 01:04:23,840 Abhay Vasant Ashtekar: it's a very nice, automatically clean thing. 718 01:04:23,900 --> 01:04:24,509 but 719 01:04:24,820 --> 01:04:30,110 Abhay Vasant Ashtekar: physically is the point of view that's supposing I've given really some state of the gravitational field. 720 01:04:30,250 --> 01:04:33,860 Abhay Vasant Ashtekar: and it is really a presented by some spin that to work to begin with. 721 01:04:34,560 --> 01:04:35,879 Abhay Vasant Ashtekar: that somehow. 722 01:04:37,240 --> 01:04:41,880 Abhay Vasant Ashtekar: if there is type, there is a physical time evolution in presence of curvature. 723 01:04:42,780 --> 01:04:48,980 Abhay Vasant Ashtekar: I mean, you're not there. You're not telling us the physical time evolution. But I come from outside and say, Well. 724 01:04:49,560 --> 01:04:57,329 Abhay Vasant Ashtekar: in us is going to this particular solution of quantum gravity solution is going to evolve in presence of curvature. 725 01:04:57,990 --> 01:05:00,559 Abhay Vasant Ashtekar: and therefore you are saying that well, if that happened. 726 01:05:00,780 --> 01:05:04,180 Abhay Vasant Ashtekar: then indirectly, you, you'll come and say that. Well. 727 01:05:04,770 --> 01:05:06,810 Abhay Vasant Ashtekar: there's going to be entertainment generated 728 01:05:06,880 --> 01:05:09,590 Abhay Vasant Ashtekar: between the subsystems that we defined. 729 01:05:10,650 --> 01:05:12,100 Abhay Vasant Ashtekar: Is that the idea? I would 730 01:05:12,560 --> 01:05:15,290 Abhay Vasant Ashtekar: Oh, or the physical idea. 731 01:05:16,180 --> 01:05:19,819 Qian Chen: Yeah, the physical, the physical idea is, try to. 732 01:05:20,040 --> 01:05:25,489 Qian Chen: It is try to, because we call loop converity is a background, independent proposal. 733 01:05:25,660 --> 01:05:32,850 Qian Chen: and we don't have any. We don't have any background. Geometry, so we don't have any. We don't have any 734 01:05:33,240 --> 01:05:37,390 Qian Chen: we don't have any. We don't have any notion of quantum geometry 735 01:05:38,000 --> 01:05:38,919 Qian Chen: so 736 01:05:39,150 --> 01:05:44,740 Qian Chen: but but but we but but as as fast I can consider 737 01:05:44,790 --> 01:05:48,659 Qian Chen: that we have a relation of prosperity which emphasize 738 01:05:48,860 --> 01:05:56,830 Qian Chen: the the relation between subsystem. So we can define, we can define the quantum geometry or 739 01:05:56,960 --> 01:06:03,039 Qian Chen: geometrical notion from the from the relational perspective at the end of the most 740 01:06:03,670 --> 01:06:17,509 Qian Chen: most direct, the a straightforward way to to have for to have a relation of prosthetics is to consider the entanglement between the between Hib. This here but here but the subway. 741 01:06:17,850 --> 01:06:24,290 Qian Chen: So so I try to. I try to. I try to connect. I try to connect the relation 742 01:06:24,310 --> 01:06:26,189 Qian Chen: of entanglement 743 01:06:26,260 --> 01:06:27,270 Qian Chen: and 744 01:06:27,400 --> 01:06:28,689 Qian Chen: quantum geometry. 745 01:06:29,090 --> 01:06:32,490 Qian Chen: So that's why I choose to study the entanglement. 746 01:06:33,800 --> 01:06:37,080 Abhay Vasant Ashtekar: That that's right. But is that the physical idea that 747 01:06:38,100 --> 01:06:43,939 Abhay Vasant Ashtekar: I give you some state of quantum privacy. It says, like, I give you some spin network. 748 01:06:44,050 --> 01:06:47,049 Abhay Vasant Ashtekar: Oh, yeah, actually make any evolution. 749 01:06:47,510 --> 01:06:50,809 Abhay Vasant Ashtekar: And if that's been there to work has not to hold on on this 750 01:06:50,850 --> 01:06:54,140 Abhay Vasant Ashtekar: we would say that well, physically, that corresponds to 751 01:06:54,390 --> 01:06:55,870 Abhay Vasant Ashtekar: encoding some curvature. 752 01:06:56,430 --> 01:06:57,439 Abhay Vasant Ashtekar: and then 753 01:06:57,570 --> 01:07:00,040 Abhay Vasant Ashtekar: or aren't you saying that somehow. 754 01:07:01,420 --> 01:07:03,760 Abhay Vasant Ashtekar: if there are these non-trivial holoma means. 755 01:07:04,010 --> 01:07:04,779 Abhay Vasant Ashtekar: then 756 01:07:05,440 --> 01:07:07,550 Abhay Vasant Ashtekar: the subsystems will get them tangled. 757 01:07:08,440 --> 01:07:12,309 Abhay Vasant Ashtekar: So I am talking about futuristic point of view. I mean, this is kind of 758 01:07:12,500 --> 01:07:14,549 Abhay Vasant Ashtekar: mathematical facts here. But 759 01:07:14,740 --> 01:07:17,069 Abhay Vasant Ashtekar: point of view of physical application 760 01:07:17,240 --> 01:07:22,530 Abhay Vasant Ashtekar: would be that. Well, if you give me the initial state, and that corresponding to such a flat space. 761 01:07:23,410 --> 01:07:27,100 Abhay Vasant Ashtekar: then would you say that that means that as time evolved. 762 01:07:27,830 --> 01:07:31,439 Abhay Vasant Ashtekar: this entitlement operator, if you like, will be trivial. 763 01:07:31,790 --> 01:07:35,889 Abhay Vasant Ashtekar: It's just. There's no in there. There's no hologram is all trivial is identity. 764 01:07:36,260 --> 01:07:39,950 Abhay Vasant Ashtekar: and then subsystems would not be evolved. It would not be entangled. 765 01:07:40,570 --> 01:07:41,279 Abhay Vasant Ashtekar: But 766 01:07:41,450 --> 01:07:43,640 Abhay Vasant Ashtekar: if there was curvature in the initial State. 767 01:07:43,970 --> 01:07:47,980 Abhay Vasant Ashtekar: and somehow somebody gives you a lot of evolution of this initial state 768 01:07:48,580 --> 01:07:51,000 Abhay Vasant Ashtekar: with respect to some internal clock, for example. 769 01:07:51,070 --> 01:07:53,039 Abhay Vasant Ashtekar: then under that evolution. 770 01:07:53,470 --> 01:07:54,950 Abhay Vasant Ashtekar: if there was 771 01:07:55,230 --> 01:07:59,159 Abhay Vasant Ashtekar: subsystems to get an entangled. I mean, i'm trying to understand the physical message. 772 01:08:00,010 --> 01:08:05,540 Qian Chen: if I want. If you want to look at a physical message, I I can 773 01:08:05,920 --> 01:08:16,580 Qian Chen: let me. Let let me give you a very simple example. Oh, for example, I can consider a 2 particle interrupt to each other by nude and gravity. 774 01:08:16,770 --> 01:08:18,389 Qian Chen: and in these cases 775 01:08:18,640 --> 01:08:28,030 Qian Chen: you you are going to have with some correlation function or for a reality system, and you can. You can find that this relative distance 776 01:08:28,580 --> 01:08:31,460 Qian Chen: encode the information of entanglement. 777 01:08:31,790 --> 01:08:34,360 Qian Chen: So in these cases we don't have any 778 01:08:34,680 --> 01:08:36,769 Qian Chen: a spin that spinner. 779 01:08:36,910 --> 01:08:44,030 Qian Chen: but we have some we have, we we have, for we have we have a basic notion of for this and the entanglement? 780 01:08:44,279 --> 01:08:51,050 Qian Chen: So in this sense I can try to. I can try to reconstruct it. The distance from the entanglement. 781 01:08:52,460 --> 01:08:57,199 Qian Chen: So this system, this is the physicist. This is the physical motivation. 782 01:08:59,850 --> 01:09:01,350 Abhay Vasant Ashtekar: So you're saying that you can 783 01:09:01,560 --> 01:09:03,789 Abhay Vasant Ashtekar: reconstruct curvature from Nintendo. 784 01:09:04,410 --> 01:09:06,010 Abhay Vasant Ashtekar: Yeah. 785 01:09:06,180 --> 01:09:07,210 Qian Chen: Yeah, yeah. 786 01:09:07,630 --> 01:09:09,579 Abhay Vasant Ashtekar: Is that what you're saying? Okay, yeah. Okay. 787 01:09:10,120 --> 01:09:13,920 Qian Chen: yeah, yeah, yeah, this is the goal of this talk. 788 01:09:15,050 --> 01:09:20,489 Abhay Vasant Ashtekar: But you can also do the other way around, right? And you can just say that in a in part example, you told me 789 01:09:20,680 --> 01:09:21,709 Abhay Vasant Ashtekar: that I got 790 01:09:21,960 --> 01:09:29,540 Abhay Vasant Ashtekar: this this interaction, which is the interaction Hamiltonian, which is the coulomb, one upon r, one minus r, 2 791 01:09:29,720 --> 01:09:31,299 Abhay Vasant Ashtekar: potential, and that 792 01:09:31,560 --> 01:09:34,440 Abhay Vasant Ashtekar: generates and time I mean the cause and effect 793 01:09:34,529 --> 01:09:35,389 you can. 794 01:09:35,609 --> 01:09:40,290 Abhay Vasant Ashtekar: We can switch right. We can say that entangle many generated by this particular 795 01:09:40,529 --> 01:09:43,270 Abhay Vasant Ashtekar: the Newtonian potential. 796 01:09:43,800 --> 01:09:47,200 Abhay Vasant Ashtekar: So you're also one could say that entanglement is generated. 797 01:09:47,399 --> 01:09:48,300 Abhay Vasant Ashtekar: My 798 01:09:48,630 --> 01:09:50,399 Abhay Vasant Ashtekar: the 799 01:09:50,800 --> 01:09:57,329 Abhay Vasant Ashtekar: by the presence of curvature in the initial state. If the initial State had no curvature, then entanglement would not be generating. 800 01:09:57,680 --> 01:09:59,730 Abhay Vasant Ashtekar: The initial State had curvature 801 01:09:59,770 --> 01:10:00,490 Abhay Vasant Ashtekar: then 802 01:10:00,660 --> 01:10:03,169 Abhay Vasant Ashtekar: by initial, I mean physical emission. Now. 803 01:10:04,040 --> 01:10:05,570 actually 804 01:10:06,280 --> 01:10:25,659 Qian Chen: actually I I I I I I didn't say that the the initial state have have Have I have no Covid. I I just want to say that the curvature is scary fat in the entanglement. Hesitation is is based on some initial state which have to know any entanglement. 805 01:10:27,450 --> 01:10:28,019 Bye. 806 01:10:28,090 --> 01:10:30,499 Abhay Vasant Ashtekar: I I think we're not communicating. Okay, Thank you. 807 01:10:30,940 --> 01:10:32,420 Qian Chen: Yeah, yeah, you're welcome. 808 01:10:34,300 --> 01:11:01,590 Western: Hi, I i'm gonna ask a question regarding the connection with the Black Hole line to be. Because so you started with a graph that it's a very similar to the kind of things that are considered when you you have a the colourizon with punctures. But I was wondering if in the end of your procedure, can you see that your calculation leads to an area low. 809 01:11:01,600 --> 01:11:07,280 Western: and not just that, but in a deal with the location corrections as we have for black holes. 810 01:11:07,550 --> 01:11:22,760 Qian Chen: Hmm. In this talk I didn't. I didn't show you. I didn't show you. But actually I seen I have some. I have some relation. I I have some intuition about about this question. yeah, since you mentioned the area law, and I can show you that, 811 01:11:22,860 --> 01:11:24,449 Qian Chen: due to the coast grinning. 812 01:11:25,400 --> 01:11:26,910 Qian Chen: you can see that 813 01:11:27,000 --> 01:11:35,670 Qian Chen: that that that the entanglement will depend on some boundary spin, and the loop is spin and this loopy. This loopy spin 814 01:11:35,820 --> 01:11:45,939 Qian Chen: actually has something to do with the you in film world, and in this you you in finger. I remember that in this, in this paper. 815 01:11:48,170 --> 01:11:58,370 Qian Chen: and in this sense, in the in in this paper they study the you in framework, and which me that they you support your you. You have a you have a 816 01:11:58,600 --> 01:12:02,709 Qian Chen: one word is a spin level, and you have some open. 817 01:12:02,820 --> 01:12:07,199 Qian Chen: You have some open edge, and then you you look at the in the toilet space. 818 01:12:07,230 --> 01:12:13,800 Qian Chen: You you look at it in the twentieth way of this vertices, and then you are going to have some area law 819 01:12:13,970 --> 01:12:16,570 Qian Chen: if you make some assumption. 820 01:12:16,730 --> 01:12:19,289 Qian Chen: And and now in in my 821 01:12:19,400 --> 01:12:21,969 Qian Chen: in this study, I can show you 822 01:12:22,000 --> 01:12:25,409 Qian Chen: that order, for all the information for entanglement 823 01:12:26,940 --> 01:12:31,530 Qian Chen: is carried by the loopy by the loopy spin and the boundary spin. 824 01:12:31,980 --> 01:12:43,889 Qian Chen: So you can imagine you can imagine a 2 vertices of a two-week voltage graph and they are many, many edge arbitrary arch link to each other. And then you study the entanglement 825 01:12:44,140 --> 01:12:47,690 Qian Chen: between the 2 edge. And now you you. 826 01:12:47,790 --> 01:12:53,589 Qian Chen: This study, will tell you that this study will tell you that in 827 01:12:53,830 --> 01:12:57,129 Qian Chen: entanglement will depend on the will depend on the 828 01:12:57,260 --> 01:13:02,410 Qian Chen: your depend depend on the on the model of you and feature. 829 01:13:03,750 --> 01:13:10,530 Qian Chen: and the the issue is, Try to remove the loopy, try, try to remove the loopy, the 830 01:13:10,550 --> 01:13:12,080 Qian Chen: the the bulk loop. 831 01:13:13,300 --> 01:13:16,660 Qian Chen: So it's possible to have a aerial law. 832 01:13:18,800 --> 01:13:19,690 Western: Okay. 833 01:13:19,750 --> 01:13:30,000 Western: it seems so I I i'm struggling a bit, because when you were mentioning this graph with tunnels and 834 01:13:30,040 --> 01:13:45,580 Western: and many meetings attach it to them. and connected with just oneing seems a bit of the opposite situation with respect to what you have with the black holes. So i'm confused the how you physically interpret the one situation with respect to the other. 835 01:13:45,710 --> 01:13:55,650 Western: but but but but but but but but so you're saying that that there is a way from what you have to connect to to to the caller that results there is 836 01:13:56,460 --> 01:13:58,730 Qian Chen: you made this graph. 837 01:13:59,180 --> 01:14:02,300 Western: Yeah, I mean, this is what you were referring to. Right? 838 01:14:02,710 --> 01:14:03,939 Qian Chen: Yeah, yeah, yeah. 839 01:14:04,240 --> 01:14:13,249 Qian Chen: I I I I I I to emphasize this is just a very particular cases, and some conclusion can be generalized. 840 01:14:14,350 --> 01:14:24,449 Western: Okay. So I mean, this will be probably a very interesting continuation of your project. This is something we need to see from what you're hand done. So thank you. 841 01:14:24,990 --> 01:14:26,009 Qian Chen: Yeah, you're welcome. 842 01:14:27,060 --> 01:14:27,880 You book 843 01:14:38,470 --> 01:14:39,469 Jorge Pullin: and the others. 844 01:14:43,440 --> 01:14:53,359 Deepak Vaid: yeah, Hi. So I have one question this the fact that this entire this of Colombia operator is entangling wasn't. It noticed by anybody before this. 845 01:14:53,900 --> 01:14:55,070 Qian Chen: Oh, sorry. 846 01:14:56,040 --> 01:14:58,390 Deepak Vaid: The fact that this Holonomy operator 847 01:14:58,830 --> 01:15:01,530 Qian Chen: Yeah, he's an entangling operator. 848 01:15:01,710 --> 01:15:02,630 Qian Chen: Yeah. 849 01:15:02,990 --> 01:15:07,300 Deepak Vaid: this. This fact was not noticed by anybody prior to your work. 850 01:15:07,760 --> 01:15:11,900 Qian Chen: I think this is a very DC. Did. This entangling 851 01:15:12,070 --> 01:15:15,199 Qian Chen: property is very, very straightforward. 852 01:15:15,560 --> 01:15:24,379 Deepak Vaid: No, I know. I know I know it's a beautiful property, but i'm just wondering if if if if anybody else had mentioned it in the in the literature in the past. 853 01:15:27,080 --> 01:15:29,650 Qian Chen: I I I don't know. Actually, I don't know. 854 01:15:30,080 --> 01:15:40,070 Qian Chen: I don't know. But I think this is a very. This is a very straightforward this. You can create some principles. Position. 855 01:15:40,470 --> 01:15:50,219 Qian Chen: Yeah. Actually, if you find some operator? Can we a spin to a position? You will we? You will. The 2 Sounds 856 01:15:50,290 --> 01:15:51,940 Qian Chen: entertainment institution 857 01:15:54,320 --> 01:15:56,449 Qian Chen: and the special. 858 01:15:56,650 --> 01:16:02,629 Qian Chen: the Loop polynomial operator is special because you prefer the gauge equivalence 859 01:16:02,970 --> 01:16:05,720 Qian Chen: How to so the gauge Invariance. 860 01:16:06,830 --> 01:16:07,750 Deepak Vaid: Right? 861 01:16:09,910 --> 01:16:16,230 Deepak Vaid: Right? No, I mean, i'm. This is very simple and straightforward, but it's also very, very beautiful, and 862 01:16:16,350 --> 01:16:19,300 Deepak Vaid: i'm just surprised that nobody noticed it in the past. 863 01:16:21,430 --> 01:16:24,949 Deepak Vaid: or maybe they did. I don't know but yeah, it's very nice 864 01:16:30,040 --> 01:16:31,280 Jorge Pullin: any other questions. 865 01:16:36,770 --> 01:16:38,400 Oh, goodness, thank you, Speaker again. 866 01:16:39,440 --> 01:16:40,619 Qian Chen: Oh, thank you.