0 00:00:02,380 --> 00:00:08,750 Jorge Pullin: Okay. So our speaker today is Patricia Rivas met Theiri, who will speak about how ubiquitous is entanglement. And Kirsty. 1 00:00:10,260 --> 00:00:16,510 Patricia Ribes Metidieri: Okay? Well, first of all. Thank you very much for giving me the opportunity to talk here today. 2 00:00:16,620 --> 00:00:24,710 Patricia Ribes Metidieri: The work i'm going to present is a work that I've done, together with my Bhd. 3 00:00:24,890 --> 00:00:29,220 Patricia Ribes Metidieri: And also we do wonderful collaborate to some friends, and they meet recently. 4 00:00:29,770 --> 00:00:37,400 Patricia Ribes Metidieri: And this talk i'm going to what the project i'm going to discuss today is based on this paper here in. 5 00:00:37,830 --> 00:00:43,740 Patricia Ribes Metidieri: So yeah, and that's I will just tell you what this talk is to me about. 6 00:00:44,480 --> 00:00:48,140 Patricia Ribes Metidieri: I think 7 00:00:48,860 --> 00:00:58,450 Patricia Ribes Metidieri: so. I will first talk what? Give a brief motivation for the topic I'm going to talk about Basically, in. 8 00:00:58,710 --> 00:01:04,690 Patricia Ribes Metidieri: Then I will give you some details of how do we compute and time, I will present some results. 9 00:01:04,780 --> 00:01:16,860 Patricia Ribes Metidieri: and if time permits, I will explain nice application of the the differences that we are going to use. or a measuring or computing environment in the 10 00:01:17,310 --> 00:01:30,370 Patricia Ribes Metidieri: so. as a matter of motivation, let me start by by reminding everybody of a surprising property of. and that surprising property is the content of the risk- that the 11 00:01:30,740 --> 00:01:33,940 Patricia Ribes Metidieri: so let's consider. Please scale up in 12 00:01:34,020 --> 00:01:40,380 Patricia Ribes Metidieri: in a one plus the dimension I mean cost is based on where i'm going to be. Not by it. It's silver space. 13 00:01:40,660 --> 00:01:50,880 Patricia Ribes Metidieri: I'm. I'm going to consider the descent of what's mute p of circles localized in space. which our code can be fine as this. 14 00:01:51,100 --> 00:02:04,100 Patricia Ribes Metidieri: What this end is as meeting function of contact support one that is, I would say, in Britain. Only reasonable is that states of this one here. 15 00:02:04,240 --> 00:02:07,700 Patricia Ribes Metidieri: where this State, he says, the negotiations 16 00:02:07,730 --> 00:02:11,340 Patricia Ribes Metidieri: are sufficient to generate the 17 00:02:12,440 --> 00:02:17,430 Patricia Ribes Metidieri: what is not so incredibly reasonable, and it's the content of the recently the theorem 18 00:02:17,520 --> 00:02:22,390 Patricia Ribes Metidieri: is that we can still generate the full in the space of the theory 19 00:02:22,470 --> 00:02:24,670 Patricia Ribes Metidieri: with states of this form. 20 00:02:24,710 --> 00:02:32,150 Patricia Ribes Metidieri: Even if we restrict all these functions to be supported in an arbitrarily small region of space time. 21 00:02:32,970 --> 00:02:42,570 Patricia Ribes Metidieri: Okay, so, as I said as this, it might not seem so surprising. So let me give you a graphic and dramatic example of what this company means. 22 00:02:43,430 --> 00:02:48,510 Patricia Ribes Metidieri: So just let's say a picture experiment on my experiment. 23 00:02:48,600 --> 00:02:53,760 Patricia Ribes Metidieri: Let's assume that we have one from laboratory here on it. 24 00:02:54,000 --> 00:03:05,110 Patricia Ribes Metidieri: so that that can generate any one to operator. that we' not necessarily unitary operator, so you can generate whatever. 25 00:03:05,140 --> 00:03:12,300 Patricia Ribes Metidieri: as long as these operators we are generating are contain within this one. and let's part that assume 26 00:03:12,460 --> 00:03:20,920 Patricia Ribes Metidieri: that in the humor space of our period there is a particular state that contains the at the back of the room 27 00:03:21,350 --> 00:03:24,560 Patricia Ribes Metidieri: one they. 28 00:03:24,610 --> 00:03:26,570 Patricia Ribes Metidieri: my acting 29 00:03:26,590 --> 00:03:28,830 Patricia Ribes Metidieri: on the on the vacuum state 30 00:03:28,910 --> 00:03:31,270 Patricia Ribes Metidieri: with an operator that I 31 00:03:42,850 --> 00:03:59,420 Patricia Ribes Metidieri: that you know this is actually well at the first day when you hear about this it's quite shocking. But this behavior is not so. We Are we happening all something similar from quantum mechanics. So let me explain what this a behavior 32 00:03:59,550 --> 00:04:01,570 Patricia Ribes Metidieri: in one to mechanics. 33 00:04:01,860 --> 00:04:09,700 Patricia Ribes Metidieri: So let's concede that the healer spaces of 2 systems. Then i'm going to be out by H. A. And HP. 34 00:04:09,840 --> 00:04:12,540 Patricia Ribes Metidieri: Oh, they mentioned in both of them. 35 00:04:13,090 --> 00:04:20,750 Patricia Ribes Metidieri: It is well known that any state in the joint human space of the system can be written in this meal form. So like this. 36 00:04:20,890 --> 00:04:29,130 Patricia Ribes Metidieri: where this one is a basis for a Hilbert Space team, and this one is a basis for humor space. little bit. 37 00:04:29,220 --> 00:04:33,250 Patricia Ribes Metidieri: If on this coefficients I I 38 00:04:33,550 --> 00:04:37,130 Patricia Ribes Metidieri: then the steep side is called a fully and download state. 39 00:04:38,240 --> 00:04:44,740 Patricia Ribes Metidieri: What if i'm mentioning on this is because we know that if I is a point in time of state. 40 00:04:44,960 --> 00:04:52,610 Patricia Ribes Metidieri: then any state in the full delivery space on the hearing can be written in this form where this oh, okay. 41 00:04:52,670 --> 00:04:56,840 Patricia Ribes Metidieri: it's an operator acting in. 42 00:04:56,890 --> 00:05:00,450 Patricia Ribes Metidieri: and this is the identity operator in the space we. 43 00:05:01,140 --> 00:05:08,360 Patricia Ribes Metidieri: And if you look at this one, you know it seems similar to the content of the 44 00:05:08,650 --> 00:05:15,100 Patricia Ribes Metidieri: if we consider that this, but that all the days of freedom within the pantom that I was telling you about. 45 00:05:16,400 --> 00:05:24,240 Patricia Ribes Metidieri: Basically, they did this a freedom of system, a and the rest of the 46 00:05:25,120 --> 00:05:37,640 Patricia Ribes Metidieri: So i'm saying all this because an intuitive way of understanding. The content of this theorem is precisely because that an important lesson that we learn from the 47 00:05:37,730 --> 00:05:41,370 Patricia Ribes Metidieri: is that in content in theory, the vacuum stay 48 00:05:41,480 --> 00:05:44,920 Patricia Ribes Metidieri: has already a very rich and dominant structure. 49 00:05:45,340 --> 00:06:01,460 Patricia Ribes Metidieri: In other words, what the the lesson that we take from this theorem is that. moreover, this viewpoint is often reinforced by the calculations of and development entropy between Abbey and and its problem. 50 00:06:02,090 --> 00:06:04,740 Patricia Ribes Metidieri: In these calculations Basically, we take. 51 00:06:04,790 --> 00:06:11,430 Patricia Ribes Metidieri: as I put these lines in our space. Them we select compact region of these lines. 52 00:06:11,630 --> 00:06:18,280 Patricia Ribes Metidieri: and then we try to compute, and then we can communicate to them within this region and each 53 00:06:19,220 --> 00:06:32,070 Patricia Ribes Metidieri: and it is a one-on-one result that the leaders of freedom within a and in the quantifier we use to measure entanglement in this case is basically the development. 54 00:06:32,670 --> 00:06:36,180 Patricia Ribes Metidieri: and we know that it's not just that it's basically in. 55 00:06:36,960 --> 00:06:41,330 Patricia Ribes Metidieri: So another important thing that I would like to mention is that 56 00:06:41,500 --> 00:06:46,440 Patricia Ribes Metidieri: both these results that I've mentioned. So the reason that the them 57 00:06:46,490 --> 00:06:54,910 Patricia Ribes Metidieri: and the calculations of 58 00:06:55,700 --> 00:07:06,870 Patricia Ribes Metidieri: and a question I had about all this is okay. yeah, we we But well, what does this statement mean in that is. 59 00:07:07,120 --> 00:07:10,380 Patricia Ribes Metidieri: I'm going to? I mean by in that. when 60 00:07:10,430 --> 00:07:21,330 Patricia Ribes Metidieri: yeah, okay, and 1, 2 fills contain in in many, many, even if we restrict the tension to regions of space that are from, but they support it. 61 00:07:21,860 --> 00:07:30,540 Patricia Ribes Metidieri: But if we try to interact with these fields or mention them. Then we find ourselves limited by by our one physical capabilities. 62 00:07:30,630 --> 00:07:33,510 Patricia Ribes Metidieri: We often look at quantum fields. 63 00:07:33,670 --> 00:07:45,130 Patricia Ribes Metidieri: Well, we mentioned them through measuring apparatus. They're made by a finite number, even though large but finite number of pixels that I have to send them with this dreadful scheme. 64 00:07:45,580 --> 00:07:50,830 Patricia Ribes Metidieri: So that's the best. This in this picture that I have depicted here in the computer 65 00:07:50,880 --> 00:07:56,090 Patricia Ribes Metidieri: is where we kind of can extract out of this one to. 66 00:07:56,280 --> 00:08:03,300 Patricia Ribes Metidieri: So basically a final number of smear the list of freedom that our detectors can measure 67 00:08:04,320 --> 00:08:05,360 Patricia Ribes Metidieri: what all this 68 00:08:05,400 --> 00:08:11,880 Patricia Ribes Metidieri: It is also when none of the entertainment is not a property of quantum states alone. 69 00:08:12,160 --> 00:08:19,430 Patricia Ribes Metidieri: If you want to talk about an animal, then that is a property of a State, but also of a choice of a subsist. 70 00:08:20,040 --> 00:08:25,960 Patricia Ribes Metidieri: So the question that I would try to answer in this talk is whether there is an amendment 71 00:08:25,980 --> 00:08:33,890 Patricia Ribes Metidieri: between these kind of systems that are motivated from expanding. As I I showed you this people. 72 00:08:34,450 --> 00:08:38,169 Patricia Ribes Metidieri: which are then the system that I want to call in a way. Not 73 00:08:39,659 --> 00:08:45,820 Patricia Ribes Metidieri: so. Before proceeding to that, let me tell you what a choice of these subsystems would be. 74 00:08:45,870 --> 00:08:51,220 Patricia Ribes Metidieri: For where, I said, how how can we extract a single video freedom 75 00:08:51,380 --> 00:08:53,370 Patricia Ribes Metidieri: out of the? 76 00:08:53,860 --> 00:08:56,550 Patricia Ribes Metidieri: And again, we will do this through this meeting. 77 00:08:57,100 --> 00:09:05,910 Patricia Ribes Metidieri: So let's take a for space them and let's select a region of 78 00:09:06,330 --> 00:09:10,470 Patricia Ribes Metidieri: and from this region I will take as many function. Okay. 79 00:09:10,880 --> 00:09:15,500 Patricia Ribes Metidieri: which, if you want, we can understand as the sensitivity of a one single detect. 80 00:09:16,560 --> 00:09:26,560 Patricia Ribes Metidieri: then I will define a single degree of freedom of the field. My it as the following Buddha As this bit of operators. 81 00:09:26,660 --> 00:09:32,320 Patricia Ribes Metidieri: which are operators, smear in space with this is main function, and 82 00:09:34,060 --> 00:09:42,610 Patricia Ribes Metidieri: also for convenience, I will choose this function it to be normalized, since that these operators are 83 00:09:43,720 --> 00:09:47,200 Patricia Ribes Metidieri: one. So this defines a system with one. 84 00:09:47,690 --> 00:09:53,460 Patricia Ribes Metidieri: and we can also define likewise. 85 00:09:53,710 --> 00:09:59,680 Patricia Ribes Metidieri: So for 86 00:10:00,280 --> 00:10:17,120 Patricia Ribes Metidieri: take those main functions, one in it, and we can use this as winning functions to define single degrees of freedom supported in each of their regions. So the question I will ask, is, is there a 87 00:10:18,050 --> 00:10:30,040 Patricia Ribes Metidieri: But, as I will explain later, you know, this system might still be a bit too small. So this is not the only systems that we can see. I will also consider systems like this 88 00:10:30,310 --> 00:10:35,100 Patricia Ribes Metidieri: in which I'm. Going to to. 89 00:10:35,260 --> 00:10:43,390 Patricia Ribes Metidieri: and regions are. and I will pick us in the degree of freedom in what's in in each of these regions. 90 00:10:43,860 --> 00:11:01,070 Patricia Ribes Metidieri: Once I have this, I will divide this in some freedom between into groups that I have represented here with the I would try to see whether there is an 91 00:11:02,210 --> 00:11:09,390 Abhay Vasant Ashtekar: but here you did not like, say explicitly, but I think you are implicitly assuming that you are only talking about free fields 92 00:11:09,820 --> 00:11:14,920 Abhay Vasant Ashtekar: in Kansas City space. Yeah, that free, it feels important because you are doing space like wearing. 93 00:11:15,380 --> 00:11:17,820 Patricia Ribes Metidieri: Yeah, yeah, Exactly. So they I think. 94 00:11:18,770 --> 00:11:24,090 Patricia Ribes Metidieri: Yeah, this was he. Didn't: I mentioned it. 95 00:11:24,570 --> 00:11:25,380 Abhay Vasant Ashtekar: Okay. 96 00:11:29,830 --> 00:11:32,120 Patricia Ribes Metidieri: Okay. So 97 00:11:32,130 --> 00:11:35,850 Patricia Ribes Metidieri: so how do we in this case? 98 00:11:36,270 --> 00:11:39,640 Patricia Ribes Metidieri: One let's go back to the system with one degree of freedom. 99 00:11:39,770 --> 00:11:44,280 Simone SPEZIALE: Another clarification is. 100 00:11:44,320 --> 00:11:45,000 Simone SPEZIALE: and 101 00:11:45,050 --> 00:11:54,780 Simone SPEZIALE: usually for free fields we would call. When we think of degrees of freedom, we think of this say independent degrees of freedom as a 102 00:11:55,180 --> 00:12:10,820 Simone SPEZIALE: different wave, numbers of a free wave. But here what you're calling degrees of freedom is a different notion, which is somehow in my intuition. These are not necessarily independent. The use of freedom right 103 00:12:11,210 --> 00:12:22,970 Patricia Ribes Metidieri: in this case. They are the independent leaders of freedom in the sense that 2 of these things are, you know, extracted now the my special. 104 00:12:23,480 --> 00:12:26,590 Simone SPEZIALE: But then you also have you find some lattice structure? Maybe? 105 00:12:26,860 --> 00:12:31,450 Patricia Ribes Metidieri: Yes, exactly. 106 00:12:31,580 --> 00:12:34,850 Patricia Ribes Metidieri: And 107 00:12:34,960 --> 00:12:37,850 Simone SPEZIALE: the same degree of freedom many times, I suppose. 108 00:12:38,050 --> 00:12:53,850 Patricia Ribes Metidieri: Well, the the important point here is that you know when I say that i'm using different regions of space. and i'm picking a single degree of freedom out of each of the regions a happening in each of the relations I could pick as many as I wanted. 109 00:12:54,080 --> 00:12:59,810 Patricia Ribes Metidieri: and the whether or not they are independent will depend on the function of meeting that I'm. Using right 110 00:13:00,800 --> 00:13:08,250 Simone SPEZIALE: in this case, maybe jump ahead. All your statements in the end would be heavily dependent on the form of this functions. F: 111 00:13:08,920 --> 00:13:18,560 Patricia Ribes Metidieri: Yeah, that is correct. The point of the talk is just saying that. Okay, I'm. Going to present some results based on examples. But this does not seem to be 112 00:13:18,660 --> 00:13:26,290 Patricia Ribes Metidieri: like Genen. As I will explain, some of the features that we had that i'm going to find about what what I'm going to 113 00:13:26,490 --> 00:13:27,800 Patricia Ribes Metidieri: explain needed 114 00:13:27,920 --> 00:13:34,110 Patricia Ribes Metidieri: our general features that we have for let's say you all these many passes without that. 115 00:13:34,820 --> 00:13:43,900 Patricia Ribes Metidieri: That is your right. And the kind of there is a freedom i'm considering are independent because i'm considering this and regions. But as I mentioned later. 116 00:13:44,040 --> 00:13:49,080 Patricia Ribes Metidieri: We've also considered an independent. This support in the same region. 117 00:13:49,620 --> 00:13:55,990 Patricia Ribes Metidieri: and the reasons we are going to present are basically well, let's say qualitatively the same. 118 00:13:56,350 --> 00:14:04,600 Patricia Ribes Metidieri: And it's that one to find a number of let's say it. 119 00:14:06,340 --> 00:14:07,090 Simone SPEZIALE: Thank you. 120 00:14:07,450 --> 00:14:15,370 Patricia Ribes Metidieri: Yeah. What? Yeah. Yeah. Okay. 121 00:14:15,520 --> 00:14:20,820 Patricia Ribes Metidieri: So yeah, sorry about that. Back to the system with a single degree of freedom. 122 00:14:21,130 --> 00:14:33,910 Patricia Ribes Metidieri: As I was mentioning. Yeah, basically they come to the the the main is already quite a state in front of the theory. So all the calculations I will be. Send repair to this quantum state. 123 00:14:34,330 --> 00:14:47,310 Patricia Ribes Metidieri: and one nice thing about the so that all the subsystems we find that number of most that I'm going to present are basically also option subsystems. 124 00:14:48,000 --> 00:14:54,790 Patricia Ribes Metidieri: which means, in particular that they reduce that city matrix representing this and these subsystems. 125 00:14:55,080 --> 00:15:00,480 Patricia Ribes Metidieri: Yeah, that me, it can only be described by the go by its covariance. 126 00:15:00,880 --> 00:15:02,750 Patricia Ribes Metidieri: which is basically 127 00:15:02,880 --> 00:15:07,170 Patricia Ribes Metidieri: a matrix containing the the 128 00:15:07,220 --> 00:15:10,860 Patricia Ribes Metidieri: 2 point functions. Once me at the Point functions. 129 00:15:15,130 --> 00:15:25,900 Patricia Ribes Metidieri: and the same goes for for a 2 day. Supremum, if we want to. The nice thing of the this strategy that i'm going to present as 130 00:15:26,140 --> 00:15:31,350 Patricia Ribes Metidieri: Simon I was asking, because that is in a sense equivalent to a 131 00:15:31,400 --> 00:15:38,750 Patricia Ribes Metidieri: where we do not select the degrees of freedom in advance. We basically take this 132 00:15:38,780 --> 00:15:42,980 Patricia Ribes Metidieri: no way also. And then I'm going to stretch it over with you 133 00:15:43,770 --> 00:15:49,970 Patricia Ribes Metidieri: and one in the they. The nice thing about this strategy as well is that 134 00:15:50,170 --> 00:16:00,380 Patricia Ribes Metidieri: we are going to be basically in a real quantum mechanics to introduce states and to compute also, and so that we can use all the techniques from one to that you mentioned 135 00:16:00,570 --> 00:16:11,390 Patricia Ribes Metidieri: to this. The dependence, however, is that all the reduced States, coming from a quantity theory, are mixed 136 00:16:11,450 --> 00:16:15,970 Patricia Ribes Metidieri: so that we cannot use the well they were not, and use for them an entropy 137 00:16:16,050 --> 00:16:23,210 Patricia Ribes Metidieri: to measure, and 138 00:16:23,780 --> 00:16:27,480 Patricia Ribes Metidieri: we wouldn't use instead. 139 00:16:27,800 --> 00:16:41,900 Patricia Ribes Metidieri: So for those of you who are not familiar with. Not Mac. Let me just give some one a summary of what it is. So Lock neck is an entanglement measure that is faithful for systems one versus and most. 140 00:16:42,040 --> 00:16:50,420 Patricia Ribes Metidieri: and that we can use for both pure and mixed states. By faithful I mean that the lock neck is larger than 0, 141 00:16:50,600 --> 00:17:01,460 Patricia Ribes Metidieri: if only there is. And even when I consider other types of of systems that might contain an a and and the most 142 00:17:01,760 --> 00:17:07,569 Patricia Ribes Metidieri: positive. 143 00:17:08,910 --> 00:17:19,109 Patricia Ribes Metidieri: but essentially one of the reasons why i'm interested in this, and I'm going to measure is because it is easy to appropriate for the Russian States which are the kind of states we are going to consider. 144 00:17:19,520 --> 00:17:23,550 Patricia Ribes Metidieri: So for a system within a modes plus can be. 145 00:17:23,790 --> 00:17:27,650 Patricia Ribes Metidieri: You can compute the 146 00:17:28,190 --> 00:17:36,830 Patricia Ribes Metidieri: where these, where these contexts here have nothing else than the syntactic eigenvalues of the 147 00:17:37,060 --> 00:17:44,600 Patricia Ribes Metidieri: So this object and will this 148 00:17:44,980 --> 00:17:56,610 Patricia Ribes Metidieri: when the Sigma set is the I it's not really needed that you have in mind. This kind of of equation. The important point for to remember 149 00:17:56,770 --> 00:17:59,770 Patricia Ribes Metidieri: is that 150 00:18:00,200 --> 00:18:06,230 Patricia Ribes Metidieri: if at least one of these is 151 00:18:07,770 --> 00:18:14,490 Patricia Ribes Metidieri: but also, if we are interested in the activity is because it has a nice physical interpretation. 152 00:18:14,860 --> 00:18:19,100 Patricia Ribes Metidieri: Basically, it is an 153 00:18:19,230 --> 00:18:25,590 Patricia Ribes Metidieri: so how much entanglement we can extract of a system via local operations and classical communication 154 00:18:25,850 --> 00:18:30,250 Patricia Ribes Metidieri: and production states it does, has the meaning as they entitlement post. 155 00:18:30,390 --> 00:18:37,150 Patricia Ribes Metidieri: So how many bell pairs we would need to be able to create, or 156 00:18:38,900 --> 00:18:44,480 Patricia Ribes Metidieri: it is Sigma Tilde, I'm. Confused. So can you go back to that last last slide, please? 157 00:18:44,700 --> 00:18:48,600 Abhay Vasant Ashtekar: So it's. Yeah, no, no, not the one that you are. Yeah. 158 00:18:49,820 --> 00:18:53,470 Abhay Vasant Ashtekar: Yeah, that one. So Sigma is a 159 00:18:53,900 --> 00:18:58,800 Abhay Vasant Ashtekar: It's just a 2 by 2 matrix, or 160 00:19:00,010 --> 00:19:02,340 Abhay Vasant Ashtekar: but is it just 2 by 2, or you? I got 161 00:19:03,120 --> 00:19:08,040 Abhay Vasant Ashtekar: and a and Lb are running, or many 162 00:19:08,520 --> 00:19:11,990 Abhay Vasant Ashtekar: one to a 120. Right? So Sigma is what 163 00:19:13,560 --> 00:19:27,710 Patricia Ribes Metidieri: in this case, basically in the example I presented before. This is a 4 by format, because we have to daily supreme. But I will also present more general. Let's say calculations in which the convenience meetings will be bigger than that 164 00:19:28,160 --> 00:19:31,370 Patricia Ribes Metidieri: in particular. 165 00:19:31,580 --> 00:19:36,750 Abhay Vasant Ashtekar: Okay. So I don't understand. The formula for t team is supposed to be. 166 00:19:39,900 --> 00:19:42,480 Abhay Vasant Ashtekar: This is not a tensor product. It is a direct sum. 167 00:19:42,870 --> 00:19:44,440 Patricia Ribes Metidieri: Yeah, this is. 168 00:19:45,250 --> 00:19:46,490 Abhay Vasant Ashtekar: And so 169 00:19:46,680 --> 00:19:54,600 Abhay Vasant Ashtekar: so how do you? How do you? Suddenly, Sigma Z. Up here? I'm Sigma Z. Supposed to be probably metrics. And i'm the working with this 170 00:19:54,620 --> 00:19:57,330 Abhay Vasant Ashtekar: 2 in by 2 and a large number of 171 00:19:58,810 --> 00:20:01,690 Abhay Vasant Ashtekar: dimensional back to space. 172 00:20:02,300 --> 00:20:03,540 Abhay Vasant Ashtekar: Yes. 173 00:20:04,300 --> 00:20:07,290 Patricia Ribes Metidieri: Well, basically. This 174 00:20:07,440 --> 00:20:14,160 Patricia Ribes Metidieri: well, this matrix is just basically doing the same thing as taking the. 175 00:20:14,370 --> 00:20:19,560 Patricia Ribes Metidieri: And in this case, maybe I should have mentioned that this is the 2 by 2 in the image. 176 00:20:19,680 --> 00:20:25,420 Patricia Ribes Metidieri: and i'm partially transparent, and the the last can be degrees of freedom if you want. 177 00:20:25,700 --> 00:20:29,430 Patricia Ribes Metidieri: So i'm just taking the pass at this position with respect to end meeting the Supreme 178 00:20:32,180 --> 00:20:44,120 Patricia Ribes Metidieri: so. And why the Sigma set is because the the partial transportation in the is equivalent to taking a minus sign of putting a minus sign in the moment of 179 00:20:44,460 --> 00:20:50,230 Patricia Ribes Metidieri: So this is just so. Let's say that for me these convenience meetings 180 00:20:52,270 --> 00:20:56,400 Patricia Ribes Metidieri: is the one the the symmetries. 181 00:20:56,920 --> 00:21:15,420 Patricia Ribes Metidieri: Well, that's it that i'm using a basis which I'm using this. It feels the momentum for each of the and then and then 182 00:21:15,710 --> 00:21:17,390 Patricia Ribes Metidieri: Yes, yeah. 183 00:21:17,900 --> 00:21:20,000 Patricia Ribes Metidieri: okay. Is that the you know 184 00:21:20,200 --> 00:21:21,720 Doyeon Kim: I have a question 185 00:21:21,910 --> 00:21:30,450 Doyeon Kim: so why the von Neumann the enter cannot be quantified in this case to explain the part 186 00:21:31,880 --> 00:21:41,720 Doyeon Kim: so like. Would you speak a bit more lovely. Maybe it would be that question Why, in this case the phone, knowing an entropy cannot be used. 187 00:21:42,210 --> 00:21:54,930 Patricia Ribes Metidieri: Yeah, As I mentioned the reason why these for 9, and that they cannot be used is because on the reduce stage we are going to consider. And basically 188 00:21:54,980 --> 00:21:57,570 Patricia Ribes Metidieri: of this sort 189 00:21:57,710 --> 00:22:01,580 Patricia Ribes Metidieri: they are mixed. As long as I understand 190 00:22:01,760 --> 00:22:16,880 Patricia Ribes Metidieri: one woman, andropy is upon the fire of entertainment. When the total state of the your system is up, your state. which in this case it's not going to be right, because I'm going to consider, Find out the well systems. 191 00:22:16,950 --> 00:22:20,030 Patricia Ribes Metidieri: And I thought, that is, that we define a number of 192 00:22:20,390 --> 00:22:40,570 Patricia Ribes Metidieri: for which the total state is mixed, and then I will ask whether there is an element between different parts of this subsystem. which again. our subsystems that let's say, call from this idea that we cannot really access in many, many when we are doing some experiment. But we have an immediate capability. 193 00:22:41,840 --> 00:22:43,480 Patricia Ribes Metidieri: Does this answer your question? 194 00:22:43,660 --> 00:22:45,390 Doyeon Kim: Okay. Thank you so much. 195 00:22:45,720 --> 00:22:47,050 Patricia Ribes Metidieri: I 2 of them. 196 00:22:47,810 --> 00:22:52,770 Deepak Vaid: Can. I just follow up on that really quickly, because 197 00:22:52,840 --> 00:22:58,280 Deepak Vaid: you can define the one number and entropy for any density matrix, right? I mean, you just have to choose. 198 00:23:00,660 --> 00:23:06,690 Patricia Ribes Metidieri: Yeah, you can. Another thing is whether this density, this one i'm an entity has the meaning of an 199 00:23:07,370 --> 00:23:16,600 Deepak Vaid: okay. And so you are saying that it only has meaning when the density matrix is that of a pure state that is not 200 00:23:16,950 --> 00:23:29,040 Patricia Ribes Metidieri: yeah, when i'm saying is that it has meaning as an and i'm a measures so that it 25 in time only when they thought of a system that they the state of the data system you are considering is you 201 00:23:29,530 --> 00:23:33,520 Deepak Vaid: right, because they the 202 00:23:33,790 --> 00:23:40,610 Patricia Ribes Metidieri: and you will make this partition to see if there are correlations on the coordinations between one of the 2 pass. But if there are already 203 00:23:40,830 --> 00:23:47,910 Patricia Ribes Metidieri: all the correlations coming from the mixedness and to the 204 00:23:48,810 --> 00:23:57,040 Deepak Vaid: Okay. So I mean the one number and it Doesn't: completely quant to characterize the entanglement structure of mixed it. That's what you're saying. 205 00:23:57,290 --> 00:23:58,350 Patricia Ribes Metidieri: Yes, exactly. 206 00:23:58,550 --> 00:23:59,450 Deepak Vaid: Thank you. 207 00:24:00,010 --> 00:24:00,660 Patricia Ribes Metidieri: Yeah. 208 00:24:02,190 --> 00:24:06,130 Patricia Ribes Metidieri: Okay. So yes, as I 209 00:24:06,170 --> 00:24:20,790 Patricia Ribes Metidieri: pointed out at some point, they the kind of you i'm going to take to this problem is, Have you based on examples. That's what i'm going to present. So in principle to define each of these, maybe one degrees of freedom we could use any meaning function we wanted. 210 00:24:21,210 --> 00:24:25,210 Patricia Ribes Metidieri: But i'm going to present i'm the 211 00:24:25,440 --> 00:24:34,420 Patricia Ribes Metidieri: I will for all that, as i'm presenting i'm going to use a function of these family of this meeting functions. 212 00:24:34,730 --> 00:24:40,170 Patricia Ribes Metidieri: where this 213 00:24:40,780 --> 00:24:48,950 Patricia Ribes Metidieri: such that well depending on this parameter, that I mean different shapes of these sweating functions. 214 00:24:50,160 --> 00:25:05,020 Patricia Ribes Metidieri: And this is just out of convenience, because the the nice thing of this familiar is meeting functions is that it allows us to compute the elements of the Covariance matrix Analytically, when our bills are much less 215 00:25:05,330 --> 00:25:09,860 Patricia Ribes Metidieri: in the equal or larger than 2, as I will mention. I see 216 00:25:10,470 --> 00:25:14,600 Abhay Vasant Ashtekar: this is a technical point, right? I Your Your 217 00:25:17,470 --> 00:25:22,100 Patricia Ribes Metidieri: yeah. This functions are 218 00:25:22,230 --> 00:25:25,770 Patricia Ribes Metidieri: is also linked to the differential ability class of these functions. 219 00:25:25,970 --> 00:25:34,000 Patricia Ribes Metidieri: But yeah, let's see that we also discussed that the the fact that these pensions are not smooth is. 220 00:25:34,170 --> 00:25:37,230 Patricia Ribes Metidieri: let's say not. 221 00:25:38,650 --> 00:25:42,580 Ivan Agullo: And you also have results for smooth functions. Right? 222 00:25:42,630 --> 00:25:49,930 Patricia Ribes Metidieri: Yes, we also have a so. Yeah, that's what i'm going to present 223 00:25:51,420 --> 00:25:59,000 Patricia Ribes Metidieri: have been computed with these functions. But this is just an example. We also have done all the calculations with the smooth functions, and also shown 224 00:25:59,110 --> 00:26:01,100 Patricia Ribes Metidieri: that then they. 225 00:26:01,140 --> 00:26:07,370 Patricia Ribes Metidieri: the lack of smoothness of this particular functions is not a problem, or let's say it doesn't change our 226 00:26:09,870 --> 00:26:20,100 Patricia Ribes Metidieri: Okay, so yeah reasons. Let me first talk about endowment between 2 days of freedom. That's kind of the the simplest kind of system we can consider. 227 00:26:20,460 --> 00:26:28,100 Patricia Ribes Metidieri: and one of the messages that I would like to convey is first, that development is not so easy to find as we are, you know. 228 00:26:28,450 --> 00:26:35,620 Patricia Ribes Metidieri: and second, but it becomes harder and harder to finally. with increasing number of dimensions of space. And I mentioned. 229 00:26:35,970 --> 00:26:44,020 Patricia Ribes Metidieri: So that's what I would like to present this. This results for different dimensions. First for the by one 230 00:26:44,170 --> 00:26:48,810 Patricia Ribes Metidieri: we're basically the regions. I'm. Going to consider. I Just 9 s 231 00:26:48,860 --> 00:26:56,360 Patricia Ribes Metidieri: of half men are separated by this distance. Drop in units of the radius with this hotline. 232 00:26:57,070 --> 00:27:10,630 Patricia Ribes Metidieri: and also for simplicity. I will take the same smelling function in both regions. as I will mentioned later. This is just not the only calculations we have. This is just an example to make things easier 233 00:27:10,820 --> 00:27:12,740 Patricia Ribes Metidieri: in explaining them. 234 00:27:13,440 --> 00:27:17,540 Patricia Ribes Metidieri: But then I will present some populations in the 235 00:27:17,550 --> 00:27:20,070 Patricia Ribes Metidieri: and finally also in the 236 00:27:20,910 --> 00:27:29,400 Patricia Ribes Metidieri: and, as you already mentioned, the for one is a bit special, because, yeah, we cannot really 237 00:27:29,480 --> 00:27:32,740 Patricia Ribes Metidieri: right the 238 00:27:32,840 --> 00:27:40,400 Patricia Ribes Metidieri: And so for a monthless fields. And yeah, when we will do what I will do is how we present some America. 239 00:27:41,230 --> 00:27:47,340 Patricia Ribes Metidieri: But the nice thing is that for whatever it of it 240 00:27:47,580 --> 00:27:53,370 Patricia Ribes Metidieri: we have. 241 00:27:54,870 --> 00:28:14,590 Patricia Ribes Metidieri: So the first thing we did in this case was okay for the one we computed the different elements of the Covariance matrix. and we try to see what is the behavior of the cross-correlation as a function of the separation between the 2 segments where these degrees of freedom are supported. 242 00:28:15,290 --> 00:28:20,800 Patricia Ribes Metidieri: And what we notice is that again, when this distance between the 2 regions is small. 243 00:28:21,010 --> 00:28:24,810 Patricia Ribes Metidieri: This close correlations depend on the details of this meeting function. 244 00:28:24,910 --> 00:28:30,420 Patricia Ribes Metidieri: But when this system here this distance grows, then we recover 245 00:28:30,520 --> 00:28:37,440 Patricia Ribes Metidieri: the results we were expecting. So they then they gave him. We were expecting 48.1 246 00:28:38,000 --> 00:28:48,100 Patricia Ribes Metidieri: and the same goes for the mobile information, which is basically a mention of the operations between the 2 systems, so both classical and random correlations 247 00:28:48,440 --> 00:28:54,040 Patricia Ribes Metidieri: which decay, as we expected for this dimensionality as one over the distance. 248 00:28:55,110 --> 00:28:59,230 Patricia Ribes Metidieri: So once we did this, we would finally go and compute an element. 249 00:28:59,830 --> 00:29:03,050 Patricia Ribes Metidieri: And this is one of the things 250 00:29:03,370 --> 00:29:08,710 Patricia Ribes Metidieri: so in this part. What you can see is the 251 00:29:08,840 --> 00:29:13,820 Patricia Ribes Metidieri: as a function of the the mass of the 252 00:29:13,940 --> 00:29:21,430 Patricia Ribes Metidieri: when this, a new parameter is basically the mass in units of this, of the radius of the 2 segments. 253 00:29:22,140 --> 00:29:30,500 Patricia Ribes Metidieri: and this is when the 2 segments are almost touching each other. So at the distance for almost able to do. 254 00:29:31,290 --> 00:29:34,890 Patricia Ribes Metidieri: and there are a couple of things that are in what mentioned. 255 00:29:35,100 --> 00:29:46,000 Patricia Ribes Metidieri: First of all, that we find endowment for some of this meeting functions that of the family, that I to send it some sizable. not for all of them, though so in that I will be fine. 256 00:29:46,020 --> 00:29:58,780 Patricia Ribes Metidieri: depends on the details of this meeting functions we use in particular. and this is me in conscious, if you remember them, from the she. are somehow more sensitive to what happens. 257 00:29:58,810 --> 00:30:02,620 Patricia Ribes Metidieri: and near the boundary of this section of this region here. 258 00:30:03,140 --> 00:30:13,630 Patricia Ribes Metidieri: and they they are better in. The The second thing we notice is that well, when the mask is sufficiently small. 259 00:30:13,640 --> 00:30:24,600 Patricia Ribes Metidieri: this and that is basically what which is a plateau. But as the the this is very rapidly 260 00:30:25,920 --> 00:30:34,380 Patricia Ribes Metidieri: so, then, for the for the next calculations, i'm going to show you value for for the mass of the P. In this platform. 261 00:30:35,810 --> 00:30:42,600 Patricia Ribes Metidieri: The second thing we we try to compute is, what is the behavior of the 262 00:30:42,720 --> 00:30:50,520 Patricia Ribes Metidieri: as a function of the separation of the 2 regions we are for a fixed. 263 00:30:51,000 --> 00:31:00,370 Patricia Ribes Metidieri: and what we have said is, that in this, in these pieces, where we find an amendment, it dies off very quickly with the separation within this to regions. 264 00:31:00,620 --> 00:31:07,080 Patricia Ribes Metidieri: in fact, within a 2025% of the radius, it completely doesn't in the best. 265 00:31:07,230 --> 00:31:08,640 Patricia Ribes Metidieri: Then we have something 266 00:31:09,650 --> 00:31:22,950 Patricia Ribes Metidieri: one. So okay, this is a nice but now let's see what happens if we go to so once again, as we completed the elements of the convenience matrix which in this case we can do analytical. 267 00:31:22,960 --> 00:31:25,250 Patricia Ribes Metidieri: And 268 00:31:25,550 --> 00:31:37,540 Patricia Ribes Metidieri: and once again we just check the that the press correlations between the we had, as one would expect for the 269 00:31:40,660 --> 00:31:52,210 Patricia Ribes Metidieri: and the symbols for them open information. We also they forward the expected for them. We, even 270 00:31:52,570 --> 00:31:55,890 Patricia Ribes Metidieri: for any of this meeting functions that I just showed. 271 00:31:56,780 --> 00:32:05,940 Patricia Ribes Metidieri: This was, let's say, the first hint that the amendment is maybe more in one plus 2 dimensions than it is to that one I mentioned. 272 00:32:06,900 --> 00:32:11,990 Patricia Ribes Metidieri: But okay, this is just a him. So then we need the same thing. For the 273 00:32:12,460 --> 00:32:17,920 Patricia Ribes Metidieri: once again we computed the they all the elements of the openings meetings 274 00:32:17,930 --> 00:32:28,890 Patricia Ribes Metidieri: we take that the correlations between field and and decay is expected, and long distances the same for the information. The 275 00:32:29,600 --> 00:32:35,530 Patricia Ribes Metidieri: but once again i'm sure you will not be too surprised when I tell you that we didn't. 276 00:32:37,050 --> 00:32:42,710 Patricia Ribes Metidieri: And to be honest, this was kind of a surprise, and this was not the only form of 277 00:32:42,750 --> 00:33:02,020 Patricia Ribes Metidieri: we tried to find a. And for this kind of system for many different in this meeting options without success. So then we thought, Hmm. Maybe to the use of freedom. It's just too. Maybe we need to go to higher dimensional systems in order to see whether or not there is no 278 00:33:02,580 --> 00:33:05,050 Patricia Ribes Metidieri: So we drive for the 279 00:33:05,700 --> 00:33:10,790 Patricia Ribes Metidieri: I mean in those plots. It was not clear that it was actually 0, right? It was small 280 00:33:11,170 --> 00:33:15,540 Abhay Vasant Ashtekar: for large values of a row. The entitlement, the login 281 00:33:16,140 --> 00:33:22,260 Abhay Vasant Ashtekar: in those plots was, was it identically 0? I mean within numerical errors or 282 00:33:27,060 --> 00:33:33,730 Abhay Vasant Ashtekar: so I'm. I'm. In between this to be the museum. But we thought that maybe 283 00:33:34,230 --> 00:33:36,430 Abhay Vasant Ashtekar: for a large role it is 284 00:33:36,490 --> 00:33:40,100 Abhay Vasant Ashtekar: for some value of row 285 00:33:41,940 --> 00:33:50,540 Patricia Ribes Metidieri: in the case of the and the buttery, even when row is the minimum value it can achieve, which is basically one of the reasons i'm touching it. 286 00:33:50,580 --> 00:33:57,550 Patricia Ribes Metidieri: Technically, we should not get there but the 287 00:33:57,930 --> 00:34:09,929 Patricia Ribes Metidieri: for any distance, and of course things become worse, because we, as I already mentioned, in need by one we know that whatever time and then there might be. It's going to decay very quickly with the business between the reasons. 288 00:34:10,290 --> 00:34:16,040 Patricia Ribes Metidieri: So even in the optimal case, we did not find entertainment for any of these meeting functions, we 289 00:34:16,500 --> 00:34:25,290 Patricia Ribes Metidieri: And then I was like, Hmm. Okay, what's going on? Even when we try to to put things as close together. We, I. If this main function we we think of. 290 00:34:27,400 --> 00:34:34,370 Patricia Ribes Metidieri: and that's why we start to try to, You know, tackle the the product from a different perspective by maybe having more. 291 00:34:34,770 --> 00:34:43,460 Patricia Ribes Metidieri: and see if there is some way in time. I will say the was that, you know, like the system is too small and tangible is, let's say to the 292 00:34:46,170 --> 00:34:57,220 Ivan Agullo: maybe you, you know, just addressing one of the points by the reason why. But we say I was using this concrete family of this meeting functions 293 00:34:57,450 --> 00:35:07,610 Ivan Agullo: A for presentation, because he had used many more, is because with them she has analytical calculations. So this 0 is not within the 294 00:35:07,810 --> 00:35:11,540 Ivan Agullo: Okay? So that was my question, because in the in the plots I was not. 295 00:35:11,570 --> 00:35:20,200 Abhay Vasant Ashtekar: It was like 30 meters 0. But can you just go back One slide, maybe, or 2 slides where you are on the plots. Yeah, so are there 0, the the plots, the 296 00:35:20,550 --> 00:35:21,280 Abhay Vasant Ashtekar: yeah. 297 00:35:22,140 --> 00:35:32,940 Abhay Vasant Ashtekar: So it's. It's, you know. It seems to me it's not quite 0, right? I mean, that's the this is the 298 00:35:32,980 --> 00:35:36,550 Patricia Ribes Metidieri: This is a concerning D. 8 by one. 299 00:35:36,850 --> 00:35:49,350 Patricia Ribes Metidieri: And what you can see is that. Yeah, okay. Here we find a value that is not for some configurations for all this. 300 00:35:51,480 --> 00:35:58,530 Patricia Ribes Metidieri: But okay, this is still a many countries. The nice thing of the how many of functions that I was 301 00:35:58,680 --> 00:36:00,490 Patricia Ribes Metidieri: using, as you pointed out. 302 00:36:00,570 --> 00:36:18,260 Patricia Ribes Metidieri: is that in highly dimensions we have exact analytical populations. We can for good. Exactly how much is the the 303 00:36:18,320 --> 00:36:21,820 Ivan Agullo: So can you go to the slide of of moodle information 304 00:36:22,270 --> 00:36:39,380 Ivan Agullo: for 3 dimensions or 3 dimensions? I mean you. You mentioned it. But maybe a bit flash by the point is that mutual information is a measure of total correlations, including classical correlations. 305 00:36:39,690 --> 00:36:47,960 Ivan Agullo: So this plot tells you that the 2 subsystems are correlated. But this doesn't tell you whether they are entangled or not. 306 00:36:48,500 --> 00:36:55,070 Ivan Agullo: and Patricia has computed, in addition to this plot, entanglement, and entanglement is exactly 0. 307 00:36:55,310 --> 00:36:56,220 Ivan Agullo: Therefore. 308 00:36:56,230 --> 00:37:01,040 Ivan Agullo: this moodle information contains just the classical correlations that that's the point. 309 00:37:02,000 --> 00:37:09,820 Abhay Vasant Ashtekar: Yeah, yeah, it's just that from the plot. It was like 30 meters 0. So okay. But the this analytical calculation is good good for me to 310 00:37:09,930 --> 00:37:12,480 Abhay Vasant Ashtekar: know that analytically design integral is 0. 311 00:37:13,700 --> 00:37:25,390 Simone SPEZIALE: And I was wondering for the non analytical part in which we explore different as meeting functions. I suppose you also consider non spherically symmetric ones. 312 00:37:25,910 --> 00:37:42,610 Patricia Ribes Metidieri: Okay, this will come later. No, no, no, okay, so let's see that in a well, more than 1 2 3 dimensions. Let's say that the America calculations become quite involved really, quickly. 313 00:37:42,650 --> 00:37:59,790 Patricia Ribes Metidieri: So we basically chose most of the calculations for simplicity, simply because, let's say we have. You could do toy model in one D. Okay, no. But you could take them as symmetric between left and right in one D. Could you do that? 314 00:38:00,830 --> 00:38:06,390 Patricia Ribes Metidieri: Hmm. I think so. Yeah. I think it it would be possible and 315 00:38:07,240 --> 00:38:09,010 Patricia Ribes Metidieri: sorry. Say it again. 316 00:38:09,280 --> 00:38:17,330 Simone SPEZIALE: it making them in one d as he made it between left and right. Was this part of the space of possibilities you explored? 317 00:38:19,190 --> 00:38:30,740 Patricia Ribes Metidieri: Let's see that in one day we were happy with funding, and then I mean quite easily, even though it is, we find an entertainment for a very peculiar. Some of these functions are not whatever 318 00:38:30,900 --> 00:38:31,700 Patricia Ribes Metidieri: and what. 319 00:38:31,850 --> 00:38:37,420 Patricia Ribes Metidieri: and then, you know, like we didn't find. But we didn't think it was so 320 00:38:38,420 --> 00:38:39,890 Patricia Ribes Metidieri: let's say, yeah. 321 00:38:40,450 --> 00:38:48,510 Patricia Ribes Metidieri: Well, let's see, I I don't think I computed as symmetric as many functions in one day. But yeah, it could be, you know. 322 00:38:49,000 --> 00:38:58,670 Patricia Ribes Metidieri: and I think then, what the the result would be is that depending on how much these functions can explore, that they, the boundary between the 2 that would change or not. 323 00:38:58,910 --> 00:39:03,150 Patricia Ribes Metidieri: because in the end. And this when we see for this, this ring, function, system 324 00:39:03,490 --> 00:39:14,720 Patricia Ribes Metidieri: and dynamic, seems to be sensitive to the behavior that they have close to the boundary situations in the case so quickly that the moment you know that you change something in a minute it's not going to. 325 00:39:15,170 --> 00:39:20,880 Abhay Vasant Ashtekar: Why do you think? Why do you think spherical symmetry has anything to do with anything? I mean 326 00:39:21,310 --> 00:39:30,530 Simone SPEZIALE: some of these? I'm wondering if some of the features that they're pointing out have anything to do with this special choice. 327 00:39:30,540 --> 00:39:35,080 Simone SPEZIALE: and whether the things could look different 328 00:39:35,180 --> 00:39:54,680 Patricia Ribes Metidieri: if such special choice was no made, then then then, then, but they said, we'll show all the results that may answer your question. Okay. And as I was going to mention, we will on. I will also show all that in another V. Some which we try, some all the configuration, like shell, like configurations 329 00:39:54,750 --> 00:39:57,290 Patricia Ribes Metidieri: in which we do manage to. 330 00:39:57,350 --> 00:40:08,270 Patricia Ribes Metidieri: But the point is not whether we find it or not, we know it is, then it's just that it's difficult to find in the sense that we still need to be very careful and fine tuning parameters in order to find 331 00:40:08,720 --> 00:40:14,100 Patricia Ribes Metidieri: The main point of the talk is that you know, finding and time, and we find a dimension of systems. 332 00:40:14,180 --> 00:40:16,010 Patricia Ribes Metidieri: It's not as easy as we thought it would be. 333 00:40:17,560 --> 00:40:29,580 Patricia Ribes Metidieri: And yeah, I agree with you that spinning our symmetry is a particular choice, but I think it's still good enough to show most of the let's see most of the conclusions of this study. 334 00:40:30,920 --> 00:40:33,250 Deepak Vaid: But yeah, there is one 335 00:40:33,540 --> 00:40:37,920 Deepak Vaid: one question that what if You' what if you turn on interactions 336 00:40:38,040 --> 00:40:40,850 Deepak Vaid: and you turn them on very, very slowly. 337 00:40:41,500 --> 00:40:42,660 Deepak Vaid: And then I 338 00:40:42,790 --> 00:40:46,150 Deepak Vaid: right? And the moment you turn interactions on 339 00:40:46,260 --> 00:40:47,050 Patricia Ribes Metidieri: Yes. 340 00:40:48,860 --> 00:40:55,780 Deepak Vaid: is it possible that that that no matter how week your interactions are, you certainly do develop in time moment. 341 00:40:56,570 --> 00:40:58,050 Patricia Ribes Metidieri: Okay. 342 00:40:58,690 --> 00:41:05,290 Patricia Ribes Metidieri: to be honest, I have not explored this, but all the results i'm presenting I just for 343 00:41:05,330 --> 00:41:14,620 Deepak Vaid: right. Right? Right? No. So I I mean, I hope you understand what i'm saying that that you know, if there's a possibility that no matter how week the interaction is 344 00:41:15,040 --> 00:41:15,880 Patricia Ribes Metidieri: based. 345 00:41:16,320 --> 00:41:18,860 Deepak Vaid: you you turn it on and 346 00:41:18,930 --> 00:41:31,720 Ivan Agullo: boom. You get lots of entertainment, so maybe the back. I I I think you is a good question. Of course I don't think that is, that is the case. Of course we haven't. We haven't checked it because interrupting field theories are. 347 00:41:31,830 --> 00:41:32,520 Ivan Agullo: I mean. 348 00:41:32,660 --> 00:41:50,670 Ivan Agullo: normally at only solved, but derivatively so it's very difficult to to check. But all this entanglement, the structure of your theory, as being you know, at the formal level, has been a study in both free and interacting theories and via these re-established theorems and and and all that ourselves. 349 00:41:50,680 --> 00:41:58,130 Ivan Agullo: And and it is accepted that you know the code of entanglement in one of the 30 is already included in 350 00:41:58,420 --> 00:41:59,970 Ivan Agullo: in in the free theory. 351 00:42:00,070 --> 00:42:18,570 Ivan Agullo: and and and and you know all all analysis, formal analysis on entertainment, You know a. A. You know the accumulated knowledge indicates, and strongly that interactions will will not change this, this basic, a feature of the field theory. 352 00:42:18,570 --> 00:42:23,590 Ivan Agullo: But of course you know, checking it at the level of calculations is is very challenging. 353 00:42:23,760 --> 00:42:24,330 Deepak Vaid: Yeah. 354 00:42:25,510 --> 00:42:26,330 Deepak Vaid: Thanks. 355 00:42:30,100 --> 00:42:30,950 Patricia Ribes Metidieri: Okay. 356 00:42:33,530 --> 00:42:44,750 Patricia Ribes Metidieri: what? So as I was saying, way in which you can try to increase the chances to plan and time, and you simply by considering systems with larger number of. 357 00:42:45,160 --> 00:42:53,230 Patricia Ribes Metidieri: and for the that, the strategy or not to be quite prolific. And we found several examples 358 00:42:53,400 --> 00:43:06,750 Patricia Ribes Metidieri: where it is basically what we find in. I will just mention 2 of these configurations that I find particularly interesting. One of them is basically the configuration that I've depicted here. 359 00:43:06,870 --> 00:43:17,490 Patricia Ribes Metidieri: where we take to end the release of freedom. Then I'm: basically supported and completely supported within these seconds. 360 00:43:17,660 --> 00:43:21,570 Patricia Ribes Metidieri: And we divide these 361 00:43:21,890 --> 00:43:35,020 Patricia Ribes Metidieri: the degree degree cycles on the web cycles, and we try to. between the Davis of freedom to one of the systems involving the 362 00:43:35,190 --> 00:43:39,200 Patricia Ribes Metidieri: that contains all the needs of freedom supported in the Reds. 363 00:43:39,670 --> 00:43:45,910 Patricia Ribes Metidieri: What the we find 2 things. The first one is that the enrollment in cases linearly 364 00:43:46,060 --> 00:43:49,230 Patricia Ribes Metidieri: with the number of 365 00:43:49,740 --> 00:44:00,960 Patricia Ribes Metidieri: and the second, and that's the one that I find most interesting, even though it's not very well appreciated here is that you need a minimum number of 366 00:44:01,300 --> 00:44:08,180 Patricia Ribes Metidieri: in this particular example. The minimum number of these days of premium is 4, but that's a a particular example. 367 00:44:09,410 --> 00:44:14,120 Patricia Ribes Metidieri: and our configuration that, I also think, is quite interesting. He's in 368 00:44:14,210 --> 00:44:29,150 Patricia Ribes Metidieri: this kind of configuration, in which we take as one subsystem a single in your freedom, completely supported in this conversation. and we start adding, the is of freedom 369 00:44:29,170 --> 00:44:41,650 Patricia Ribes Metidieri: as close as possible. and once again, we have the same kind of input. So for the equal to. we still need how many number of 370 00:44:41,910 --> 00:44:47,240 Patricia Ribes Metidieri: in this particular case. 371 00:44:47,660 --> 00:44:52,580 Patricia Ribes Metidieri: But that, again, is a feature that depends on how this meeting actually. 372 00:44:53,070 --> 00:45:00,060 Patricia Ribes Metidieri: and the other thing that we see that is, that is, that the entertainment Saturday week. 373 00:45:00,110 --> 00:45:09,720 Patricia Ribes Metidieri: when we continue having. as I mentioned before, one of the things we observe about them. Is it that it decays very quickly with this? 374 00:45:09,910 --> 00:45:19,500 Patricia Ribes Metidieri: So basically what we keep adding more than this freedom around the center one. Let's say that the other link is, basically do not change in time on them 375 00:45:19,560 --> 00:45:22,690 Patricia Ribes Metidieri: with the 376 00:45:23,980 --> 00:45:24,710 Patricia Ribes Metidieri: But 377 00:45:24,930 --> 00:45:32,090 Patricia Ribes Metidieri: once again in the 3 dimensions. What we learned is that the environment is yeah, quite difficult to find. 378 00:45:32,380 --> 00:45:44,200 Patricia Ribes Metidieri: and I can tell you that we drive of the order of 17 modes, but also 379 00:45:44,220 --> 00:45:51,160 Patricia Ribes Metidieri: and also these kind of configurations, where we try to maximize the surface of contact between the 2 subsystem. 380 00:45:54,150 --> 00:46:01,470 Patricia Ribes Metidieri: But as you were pointing out. This is also a consequence of type of regions of support, and what we are. 381 00:46:02,900 --> 00:46:14,760 Patricia Ribes Metidieri: anyway. All that I have presented out in now is a very particular example. And as I mentioned, this is just because it's simpler to to explain anything I need to more clean, and we are. 382 00:46:15,000 --> 00:46:18,250 Patricia Ribes Metidieri: But this is not the only thing we have tried, not at all. 383 00:46:18,260 --> 00:46:36,650 Patricia Ribes Metidieri: We've also tried the basically May, taking more general configurations for a phenomenal. It's meeting them with different functions. It's meaning different regions with different functions, non positives, meaning functions. We need operators that are more general and take linear combinations of the momentum. 384 00:46:36,650 --> 00:46:42,100 Patricia Ribes Metidieri: All the Prime Minister's main function, and also in the we are most defined within the same regions. 385 00:46:42,210 --> 00:46:50,860 Patricia Ribes Metidieri: And what I want to say about this is is the main one from the beginning, and it's that if you take a systems with a finite number of 386 00:46:50,910 --> 00:46:57,050 Patricia Ribes Metidieri: entanglement is in general and difficult to find. and it's more difficult to do this in dimensions. 387 00:46:57,860 --> 00:47:04,060 Patricia Ribes Metidieri: Does this mean that there is no time? Not at all, absolutely not this, not what we are saying. 388 00:47:04,330 --> 00:47:16,710 Patricia Ribes Metidieri: In fact, as I mentioned in the beginning, entitlement is not a property of quantum states alone. It's a property of both the quantum state and the 2 subsystem. We make 389 00:47:17,610 --> 00:47:24,380 Patricia Ribes Metidieri: so an easy way of finding an amendment, for example, would be to just make a change of basis of these operators right? 390 00:47:24,560 --> 00:47:31,560 Patricia Ribes Metidieri: And they find new sets of operators is a by one Brian, and by one 391 00:47:31,720 --> 00:47:38,920 Patricia Ribes Metidieri: there are linear combinations of the operators they find properly supported in regions. K. And 392 00:47:39,660 --> 00:47:45,230 Patricia Ribes Metidieri: this parameter R is often called the discreasing intensity, and one can show 393 00:47:45,290 --> 00:47:52,600 Patricia Ribes Metidieri: that this subsystem, so the subsystems made of one. My, these things of freedom 394 00:47:52,850 --> 00:47:54,210 Patricia Ribes Metidieri: I didn't tell you. 395 00:47:54,400 --> 00:47:58,800 Patricia Ribes Metidieri: for all squeezing and density is larger than a. 396 00:47:59,550 --> 00:48:13,610 Patricia Ribes Metidieri: But of course you could tell me that. Yeah, this is not a very interesting example in the sense that these new degrees of freedom are a non look right because they are linear combinations of most that are properly supported in these to. 397 00:48:14,720 --> 00:48:26,030 Patricia Ribes Metidieri: But okay, this is just one way. Another way is trying to find a configuration that, as you mentioned, is not spherically semantic, and somehow tries to maximize the contact region 398 00:48:26,080 --> 00:48:30,920 Patricia Ribes Metidieri: between what we call different subsystems. That would be something like this. 399 00:48:31,060 --> 00:48:36,500 Patricia Ribes Metidieri: What we define a month here, this again spit it, and then we define other modes 400 00:48:36,540 --> 00:48:40,370 Patricia Ribes Metidieri: in a. 401 00:48:40,980 --> 00:48:43,850 Patricia Ribes Metidieri: and here it is we manage to. 402 00:48:43,960 --> 00:48:59,330 Patricia Ribes Metidieri: But the important point is not what they, what i'm finding, but that it is still quite difficult in the sense that we need to really fine tune the parameters we are using. And then this meeting functions in order to find 403 00:49:00,670 --> 00:49:02,170 Patricia Ribes Metidieri: What's that? A question? 404 00:49:05,320 --> 00:49:13,790 Patricia Ribes Metidieri: Okay. So I think that I am a bit over time. I don't know if I have time for this. Yes, go ahead. 405 00:49:14,680 --> 00:49:17,830 Patricia Ribes Metidieri: Yeah. Okay. So the same mentioned. 406 00:49:18,790 --> 00:49:23,400 Veso: Yes, I I have a quick question. 407 00:49:25,090 --> 00:49:26,070 Veso: Can you hear me? 408 00:49:26,390 --> 00:49:28,370 Patricia Ribes Metidieri: Yes, yes, please go ahead. 409 00:49:29,390 --> 00:49:34,400 Veso: So to to understand You're looking at 2.4, 2 point 410 00:49:34,490 --> 00:49:36,350 Veso: function correlations. 411 00:49:36,670 --> 00:49:48,990 Veso: and this is computed in the Minkowski vacuum isn't it. So did you try different states for the correlation function to be computed. 412 00:49:49,320 --> 00:49:51,350 Veso: I mean, rather than using the vacuum. 413 00:49:52,510 --> 00:50:03,250 Patricia Ribes Metidieri: as I mentioned at the beginning, and in this particular work we were interested in just looking at the. 414 00:50:03,470 --> 00:50:07,800 Patricia Ribes Metidieri: and we did not try any any other things. 415 00:50:08,000 --> 00:50:11,560 Patricia Ribes Metidieri: But I 416 00:50:11,960 --> 00:50:13,170 Patricia Ribes Metidieri: basically. 417 00:50:13,310 --> 00:50:16,000 Patricia Ribes Metidieri: And let's say that when 418 00:50:16,860 --> 00:50:19,840 Patricia Ribes Metidieri: yeah, we didn't try other things. But I think 419 00:50:20,010 --> 00:50:25,830 Patricia Ribes Metidieri: that the for other adoption states, for example, it will be. 420 00:50:25,880 --> 00:50:28,390 Patricia Ribes Metidieri: The situation will be 421 00:50:29,300 --> 00:50:30,490 Veso: okay 422 00:50:31,250 --> 00:50:41,750 Patricia Ribes Metidieri: regarding all the the possible states. One: yeah, we can obtain them from the bottom. So we just try to characterize the 423 00:50:42,320 --> 00:50:43,760 Patricia Ribes Metidieri: Let's see how this works. 424 00:50:44,040 --> 00:50:44,870 Veso: Thank you. 425 00:50:48,210 --> 00:51:03,360 Patricia Ribes Metidieri: Okay. So as I was mentioning a nice application of these ideas of trying to to measure and development between finite and biggest freedom is an application to compete and development in their 426 00:51:04,000 --> 00:51:12,500 Patricia Ribes Metidieri: and in particular this the motivation for this calculation that i'm going to talk about very briefly come from the theory of location. 427 00:51:12,910 --> 00:51:21,360 Patricia Ribes Metidieri: So one of the impression is one of the proposals to explain the the large, the information of the landscape that you from a universe. 428 00:51:21,560 --> 00:51:30,810 Patricia Ribes Metidieri: and one of its nice predictions is that the density perturbations that in every universe set as seeds 429 00:51:30,990 --> 00:51:35,650 Patricia Ribes Metidieri: for all this 430 00:51:37,380 --> 00:51:39,990 Patricia Ribes Metidieri: in particular. 431 00:51:40,150 --> 00:51:57,330 Patricia Ribes Metidieri: that this density perturbation originate from quantum mechanics fluctuations of the So a question that it's been on the table for a long time is okay, this is a very nice prediction. But can we test the ongoing 432 00:51:57,370 --> 00:52:09,160 Patricia Ribes Metidieri: of the cosmological density perturbations at the end of operation. and and the idea with him was to try to contribute a little bit to this discussion by trying to see 433 00:52:09,500 --> 00:52:12,350 Patricia Ribes Metidieri: when they 2 days of freedom 434 00:52:12,860 --> 00:52:16,710 Patricia Ribes Metidieri: close to the end of completion. 435 00:52:17,210 --> 00:52:23,280 Patricia Ribes Metidieri: So what i'm going to explain now is exactly the same as that. He has it for you to space them. 436 00:52:23,330 --> 00:52:27,380 Patricia Ribes Metidieri: and instead of looking at inflation, i'm going to 437 00:52:32,170 --> 00:52:41,290 Patricia Ribes Metidieri: so very briefly where I what I did was taking 2 days of freedom in the concrete parts for the center space, time. 438 00:52:41,460 --> 00:52:47,920 Patricia Ribes Metidieri: and in the in the one's previous vacuum. I'm. Trying to compute a. And 439 00:52:48,370 --> 00:52:55,770 Patricia Ribes Metidieri: And what we found is that even though there are no correlations in the 440 00:52:56,090 --> 00:52:59,520 Patricia Ribes Metidieri: are fewer than these correlations contain in them. 441 00:53:00,220 --> 00:53:12,660 Patricia Ribes Metidieri: The corporation is a bit more subtle because of the infrared divergence for. But what can still show with the logic activity in this case is finally an independent of the. 442 00:53:13,700 --> 00:53:28,370 Patricia Ribes Metidieri: And when I said with you once again. we find that there is no time for any of this meeting passes we use once again I'm. Using the same family as many functions which allows to do the calculation, and I need to be an Mexican. 443 00:53:29,050 --> 00:53:36,560 Patricia Ribes Metidieri: and what we find is something like this. So we find that the that they're in they're smaller than they're getting money 444 00:53:36,770 --> 00:53:49,740 Patricia Ribes Metidieri: for the is basically the quantity that the tenants what local activities, and or whether or not there is some time. 445 00:53:49,900 --> 00:53:51,910 Patricia Ribes Metidieri: can we read them in this form 446 00:53:52,490 --> 00:54:05,230 Patricia Ribes Metidieri: Where this time comes is exactly the same, and symptoms that we plus have different them that comes from the scaling mining part of the power. Spec. 447 00:54:05,880 --> 00:54:12,550 Patricia Ribes Metidieri: An important point is that this function here is always positive for all values of distance 448 00:54:12,560 --> 00:54:15,260 Patricia Ribes Metidieri: and for the 449 00:54:15,910 --> 00:54:22,320 Patricia Ribes Metidieri: and yeah, this one which means in particular this 450 00:54:22,680 --> 00:54:27,210 Patricia Ribes Metidieri: they 451 00:54:27,760 --> 00:54:28,840 Patricia Ribes Metidieri: in 452 00:54:29,010 --> 00:54:38,410 Patricia Ribes Metidieri: and in a sense you would think of that it would be a bit more difficult to find, even though this is not a measure of 453 00:54:39,280 --> 00:54:45,080 Abhay Vasant Ashtekar: the but the point about this the sitter or inflation would be to understand the time. Get timers right. 454 00:54:45,100 --> 00:54:49,190 Abhay Vasant Ashtekar: In other words, maybe at some time there's been some entanglement, but 455 00:54:49,400 --> 00:54:55,620 Abhay Vasant Ashtekar: what happens at later time, because the Milkowski space. Nothing changes in time, but here things do change in time. 456 00:54:55,880 --> 00:55:01,090 Abhay Vasant Ashtekar: And so it seemed to me just quickly that, in fact, the entire entertainment even 457 00:55:01,790 --> 00:55:13,080 Patricia Ribes Metidieri: reduces in time. Is that true or not? 458 00:55:13,100 --> 00:55:20,750 Patricia Ribes Metidieri: And the the relative size of this main function, so the physical size of the the regions we are looking at compared to the 459 00:55:20,860 --> 00:55:27,020 Patricia Ribes Metidieri: and I'm. 3 as the inflation proceeds. So this radius from this physical distance goes. 460 00:55:27,040 --> 00:55:31,250 Patricia Ribes Metidieri: and what becomes less likely this is that this. 461 00:55:31,380 --> 00:55:35,440 Patricia Ribes Metidieri: Let them. Yeah. This. 462 00:55:35,910 --> 00:55:47,000 Abhay Vasant Ashtekar: So yeah, we're actually quite surprised about this, because we have some idea of what it works in that the patient generates some down. 463 00:55:47,300 --> 00:55:52,430 Abhay Vasant Ashtekar: because I can from it's conformity related to the in the case space. But this is a massive scale of 464 00:55:52,600 --> 00:55:58,930 Abhay Vasant Ashtekar: it's probably related, and so the fall off with respect to the distance will be physical. Distance 465 00:55:59,150 --> 00:55:59,970 Patricia Ribes Metidieri: is. 466 00:56:00,160 --> 00:56:09,100 Abhay Vasant Ashtekar: I mean, the calculation knows about I mean casket distance, but the physical, distant changes in time. But but let me I One thing. Can you come back to the previous slide? 467 00:56:10,070 --> 00:56:15,550 Ivan Agullo: A. As as as Patricia nicely pointed out, because you know 468 00:56:15,600 --> 00:56:26,040 Ivan Agullo: a a. You know that in in the city, if you go to super Hubble distances like the 2 point function is larger than it Minkowski. In fact, it stops decaying with the distance 469 00:56:26,190 --> 00:56:32,210 Ivan Agullo: at super Hubble distances. The 2 point function goes to a constant given by the square of the Have a right. 470 00:56:32,360 --> 00:56:51,090 Ivan Agullo: so there are many more correlations in the sitter in the mind. That is vacuum; that in Minkowski space time at at black distances, at short distances they look very similar. So the word question was was whether those extra correlations, you know E. A. E. A account for the existence of entanglement. 471 00:56:51,570 --> 00:56:54,850 Ivan Agullo: and what, Patrice, your phone is the other way around. 472 00:56:55,040 --> 00:56:58,070 Ivan Agullo: What is far better away 473 00:56:58,160 --> 00:57:02,380 Ivan Agullo: from entanglement, although you know far away from 0, it is still 0, 474 00:57:02,520 --> 00:57:13,790 Ivan Agullo: a a that that that in costs. This extra correlations do not carry any quantum correlations at all, and that, for me at least, was quite surprising and unexpected. 475 00:57:15,290 --> 00:57:17,460 Abhay Vasant Ashtekar: Okay, we should discuss this later. But 476 00:57:19,930 --> 00:57:29,600 Abhay Vasant Ashtekar: I mean the thing is that you explain to us in the in a context, I mean, Kask is a difference between coral license, and I don't know. and and then 477 00:57:30,790 --> 00:57:35,020 Abhay Vasant Ashtekar: so. But maybe we should talk about That's the 478 00:57:36,570 --> 00:57:53,500 Patricia Ribes Metidieri: Okay. So yeah, this is, I I understand. I'm sorry for joining you with the time. So it just to summarize what we found with these calculations is basically that in time, when it is, it is that of course, we have some theorems that tell us that it is there. 479 00:57:53,650 --> 00:58:00,100 Patricia Ribes Metidieri: but it was more difficult to find it than we had expected, for a finite dimensional systems. 480 00:58:00,320 --> 00:58:04,230 Patricia Ribes Metidieri: and this entertainment seems to be distributed in a certain way. 481 00:58:04,650 --> 00:58:14,400 Patricia Ribes Metidieri: So what we know is that we can find it very easily, either by inv in the many which is yeah, one experimental, impossible. 482 00:58:14,770 --> 00:58:21,110 Patricia Ribes Metidieri: or that we, if we want to find it, we have to select very carefully. We are using. 483 00:58:21,460 --> 00:58:34,480 Patricia Ribes Metidieri: which, of course, is possible, but those also. Possibly it will be experimentally typical. The other thing that we we found is that the environment seems to be harder to find with increasing space, and I mentioned. 484 00:58:35,150 --> 00:58:49,610 Patricia Ribes Metidieri: and for the this application that I gave in the 6 weeks time is that one in the space, and we find more correlations, but a separate how? The super have a distances they do not seem to. 485 00:58:51,100 --> 00:58:53,850 Patricia Ribes Metidieri: So yeah, that's that's one. 486 00:58:53,890 --> 00:58:56,810 Patricia Ribes Metidieri: And I would like to thank you very much for your attention. 487 00:58:57,380 --> 00:59:01,080 Patricia Ribes Metidieri: Yeah. And we happy to answer any questions that Haven't. 488 00:59:02,530 --> 00:59:03,480 Jorge Pullin: Yeah, we are. 489 00:59:05,970 --> 00:59:08,530 Adrià Delhom i Latorre: So thanks for for the nice talk. 490 00:59:08,540 --> 00:59:13,400 Adrià Delhom i Latorre: I was wondering I don't know if it makes sense. But I was wondering how you tried to use 491 00:59:14,590 --> 00:59:22,750 Adrià Delhom i Latorre: this meeting function is that somehow the article moving with the with the they also increase. 492 00:59:23,590 --> 00:59:33,270 Adrià Delhom i Latorre: Well, that might mean that you're using different degrees of freedom at each time, Step or I don't know exactly what it would mean. But but how do you try? I'm. Curious. 493 00:59:35,240 --> 00:59:47,580 Patricia Ribes Metidieri: Well, the idea is that let's say that. And then what we' about in tunnel and in the center space is as I was mentioning days apart. That depends on what is basically the same as my 494 00:59:47,800 --> 00:59:49,970 Patricia Ribes Metidieri: but the second, the second piece 495 00:59:50,210 --> 01:00:02,940 Patricia Ribes Metidieri: depends on the physical distance, not on the removing distance, but on the physical distance for takes taken readers of the regions. So i'm pretty we are following this. This is pretty much they are increasing because of 496 01:00:03,930 --> 01:00:09,400 Patricia Ribes Metidieri: but when keeping them at the same, let's say at the same. 497 01:00:14,100 --> 01:00:16,480 Adrià Delhom i Latorre: Okay. Okay, Thank you. 498 01:00:17,020 --> 01:00:18,130 Patricia Ribes Metidieri: Cool. 499 01:00:20,060 --> 01:00:33,860 Suddhasattwa Brahma: Yeah, Hi. Thanks. Thanks for the nice stuff. I he! I just didn't understand the computation very well, I guess. So. You have this 2 patches, so you choose the time slicing so a space like hyper surface, and on that you choose to patches that correct. 500 01:00:34,200 --> 01:00:35,380 Patricia Ribes Metidieri: Yeah, that is correct. 501 01:00:35,750 --> 01:00:41,310 Suddhasattwa Brahma: And are these 2 patches within the horizon, or like? Are they separated? 502 01:00:41,950 --> 01:00:53,550 Patricia Ribes Metidieri: Okay. So the idea is that we can analyze how this 2 regions, what the the size of this, as you were mentioned in, which is a slicing, we can take different license. 503 01:00:53,630 --> 01:01:03,610 Patricia Ribes Metidieri: and the point is that if if these regions are small and well contained within the Hubble radius. then the 504 01:01:03,900 --> 01:01:11,150 Patricia Ribes Metidieri: well, we take these 2 patches to be much bigger than separated. What distances that are of the 505 01:01:11,180 --> 01:01:22,440 Patricia Ribes Metidieri: or the what we find is these extra contributions for these extra correlations that somehow make us be part of the way coming down. 506 01:01:22,670 --> 01:01:28,300 Patricia Ribes Metidieri: In a sense. For, as I mentioned, this is not a measurement of how far we are from. Okay. 507 01:01:30,040 --> 01:01:40,920 Suddhasattwa Brahma: So so they they are set. So when when you choose them to be like much more separated, like so outside the each other's horizon or something. Then then, that's the part where you find the novelty in the decision. 508 01:01:40,980 --> 01:01:44,100 Suddhasattwa Brahma: And you're finding that it's actually getting 509 01:01:44,410 --> 01:01:46,000 Suddhasattwa Brahma: smaller. Not larger. 510 01:01:46,580 --> 01:01:47,850 Patricia Ribes Metidieri: Yes, please. 511 01:01:53,630 --> 01:01:54,740 Jorge Pullin: Other questions. 512 01:01:58,780 --> 01:02:06,250 Abhay Vasant Ashtekar: Maybe you can comments a little bit about your your understanding of why. as dimension increases. 513 01:02:06,380 --> 01:02:09,110 Abhay Vasant Ashtekar: the enrollment becomes less and less. 514 01:02:09,820 --> 01:02:16,050 Patricia Ribes Metidieri: Well, basically we know the correlations decrease faster. 515 01:02:21,260 --> 01:02:31,870 Patricia Ribes Metidieri: So that is kind of fortunate with the explanation why in development decreases faster as well right they the quantum content of this and this correlations. 516 01:02:33,830 --> 01:02:36,440 Patricia Ribes Metidieri: And in the case of this 517 01:02:36,710 --> 01:02:45,050 Patricia Ribes Metidieri: yeah, so let's say, the total correlation might be K. As one over distance to a certain power that depends on the on the dimensionality of spacing. 518 01:02:45,070 --> 01:02:54,730 Patricia Ribes Metidieri: But i'm. And then, when we even more and we think the same space information. 519 01:02:54,880 --> 01:03:04,330 Abhay Vasant Ashtekar: I don't know if this is what I you wanted that we exactly that is, it's more than what you would expect from correlations. 520 01:03:04,740 --> 01:03:08,520 Abhay Vasant Ashtekar: Is there some intuitive understanding, eg. For example, that 521 01:03:09,050 --> 01:03:10,780 Abhay Vasant Ashtekar: degrees of freedom have more room 522 01:03:11,270 --> 01:03:15,840 Abhay Vasant Ashtekar: to be in time, but I mean, you know, in in the higher dimensions. 523 01:03:16,140 --> 01:03:18,940 And so you're probing a given the 524 01:03:20,210 --> 01:03:35,720 Abhay Vasant Ashtekar: you keep it going to do the same. But then. outside those radios that are more and more degrees of freedom as time goes on. Yeah. you know, we're the I I I just want you to know you're in to you. And if there was something that you understand about this. 525 01:03:35,760 --> 01:03:39,130 Abhay Vasant Ashtekar: the main dependence on the dimension 526 01:03:40,960 --> 01:03:41,770 Patricia Ribes Metidieri: Hmm. 527 01:03:46,310 --> 01:03:50,540 Abhay Vasant Ashtekar: I mean it's more than the the fall of of the 528 01:03:51,040 --> 01:03:54,000 Patricia Ribes Metidieri: Yes, yes, of course. And then the point is 529 01:03:54,300 --> 01:04:06,900 Patricia Ribes Metidieri: that I cannot really say anything. It's a. Because, as I was mentioning, we just have some examples. This is something that we what that I would say, requires part of the investigation, because people 530 01:04:07,040 --> 01:04:24,770 Patricia Ribes Metidieri: we can actually say something. Of course the the picture is is precisely what you were saying. So it correlations to keep us this, but also like we have more room for this to be subpoena to be end done with others. I don't know we are restricted to a few number of people. 531 01:04:24,820 --> 01:04:34,350 Patricia Ribes Metidieri: Well, basically yeah, there is a kind of some other things. We increase the level of mixedness, and the tang on them becomes a much harder to find. 532 01:04:34,570 --> 01:04:40,990 Patricia Ribes Metidieri: But exactly how the let's see the 533 01:04:47,120 --> 01:04:53,670 Abhay Vasant Ashtekar: I just had one small comment about it was about what I was asking about. Normally you talk about 534 01:04:53,700 --> 01:04:59,620 Abhay Vasant Ashtekar: momentum modes and degrees of freedom in that way. To me at least, I mean that is. 535 01:05:00,830 --> 01:05:07,470 Abhay Vasant Ashtekar: that is kind of localizing and momentum space. And it seems to me that localizing in physical space is much more directly used. 536 01:05:07,690 --> 01:05:17,820 Abhay Vasant Ashtekar: It's related to the lab experiments so than localizing in the moment of space. So, in fact, what is being done here is more physical. then 537 01:05:17,860 --> 01:05:20,510 Abhay Vasant Ashtekar: what the Simone was 538 01:05:20,620 --> 01:05:23,910 Abhay Vasant Ashtekar: proposing is an alternative, and I wonder if somebody has some comment on that 539 01:05:27,830 --> 01:05:33,670 Simone SPEZIALE: I see. Well. that that's true. But then 540 01:05:33,710 --> 01:05:37,450 Simone SPEZIALE: there's this finite size effect that it's a 541 01:05:38,070 --> 01:05:41,660 Simone SPEZIALE: not clear to me yet how 542 01:05:41,780 --> 01:05:58,000 Simone SPEZIALE: I mean, if you really, if you're designing spacetime, and then there's a lot. This, then we can only have, you know, different placettes. No problem. But now what we' is confusing me is that you take a a circle, send me of circles, or a family of or 543 01:05:58,020 --> 01:06:07,310 Simone SPEZIALE: and now you know, a a or a novels meeting function center in the same point. Would you call it the 2 degrees of freedom, I suppose. 544 01:06:07,390 --> 01:06:10,120 Abhay Vasant Ashtekar: But now you can run the same test. 545 01:06:10,350 --> 01:06:13,700 Simone SPEZIALE: because they are partially overlapping. So that's the kind of a 546 01:06:14,150 --> 01:06:22,050 Simone SPEZIALE: I I was thinking more of of this partial overlapping as a tricky aspect rather than going from a moment to 547 01:06:22,430 --> 01:06:24,950 Abhay Vasant Ashtekar: Yeah. But in the moment in space it is complete overlap. 548 01:06:25,620 --> 01:06:26,410 Simone SPEZIALE: Yes. 549 01:06:26,620 --> 01:06:30,790 Abhay Vasant Ashtekar: I mean, and the the my, those are either my complete or like in space. 550 01:06:30,880 --> 01:06:33,880 Abhay Vasant Ashtekar: That's right. I think that that is, I think 551 01:06:34,010 --> 01:06:36,540 Abhay Vasant Ashtekar: I don't know. 552 01:06:36,970 --> 01:06:41,190 Simone SPEZIALE: and so to keep going down design. So in the end 553 01:06:41,280 --> 01:06:58,170 Simone SPEZIALE: this difficulty of finding the the environment is not helped. If I understand correctly, or maybe me something. If you go from a a circular meeting functions to something very over, that it would simulate squeezing somehow 554 01:07:00,030 --> 01:07:01,080 Patricia Ribes Metidieri: and 555 01:07:02,410 --> 01:07:07,530 Simone SPEZIALE: sorry. Can you repeat the question 556 01:07:07,860 --> 01:07:12,380 Simone SPEZIALE: in the end. Politically, they don't depend so much on these shape that you use. 557 01:07:13,010 --> 01:07:22,320 Simone SPEZIALE: whereas very naively I was maybe thinking if, instead of the using this family of circular or sphericalismetics meetings. They are very obliged 558 01:07:22,440 --> 01:07:29,370 Simone SPEZIALE: kind of like. Maybe it would be easier to see the tanglement kind of like, you know when you have a squeezed state, but it's very naive 559 01:07:29,650 --> 01:07:39,980 Patricia Ribes Metidieri: once. It is true again, that if we try to somehow, let's say, increase the surface of of contact between what we call to the 560 01:07:40,160 --> 01:07:46,990 Patricia Ribes Metidieri: it's. In principle it's easier to panel, as in the case of these spherical shs overlapping each other. 561 01:07:47,330 --> 01:07:49,100 Patricia Ribes Metidieri: But still 562 01:07:49,270 --> 01:07:55,430 Patricia Ribes Metidieri: What we expect is that you know we not any function or not in this many fashion. 563 01:07:55,680 --> 01:08:00,050 Patricia Ribes Metidieri: I will give you 564 01:08:00,390 --> 01:08:02,780 Patricia Ribes Metidieri: fine. 565 01:08:02,900 --> 01:08:12,250 Patricia Ribes Metidieri: so you can see that it's still, because there's something more complete with the higher and surface of the contact, then it might be a bit easier. 566 01:08:12,410 --> 01:08:15,960 Patricia Ribes Metidieri: We are in 3 dimensions, so I don't think it's going to. 567 01:08:16,270 --> 01:08:24,640 Patricia Ribes Metidieri: But again for this week the picture of the squeezing you have, and I also give this example of just mixing. You look at the. 568 01:08:24,689 --> 01:08:33,689 Patricia Ribes Metidieri: and that is again. That is just the process of. 569 01:08:33,870 --> 01:08:39,240 Patricia Ribes Metidieri: and then you can find us with the squeezing that you want. But then the resulting 570 01:08:41,080 --> 01:08:48,740 Deepak Vaid: just just want to just want to clarify. I think, Simone, when you talk about squeezing right. You talk about squeezed Gaussian states, for example. 571 01:08:48,830 --> 01:08:50,859 Deepak Vaid: That's 572 01:08:51,350 --> 01:08:52,149 Simone SPEZIALE: right. 573 01:08:52,370 --> 01:09:06,620 Simone SPEZIALE: No, I I say I already was naive, I said. I'm wondering whether you know there will be some analogous that that by using shapes which are oblique, like in the case of screen states. But this is now all the confusion space. I understand it. 574 01:09:06,819 --> 01:09:09,859 Simone SPEZIALE: But to understand the answer, thank you 575 01:09:11,420 --> 01:09:19,529 Deepak Vaid: and and Patricia. I just want to say that I really like your your presentation, the the graphics and all that. It's. It's really nice. 576 01:09:20,840 --> 01:09:21,930 Patricia Ribes Metidieri: Yeah, thank you. 577 01:09:23,899 --> 01:09:24,819 Jorge Pullin: Any other 578 01:09:32,359 --> 01:09:38,090 Suddhasattwa Brahma: sorry one quick question which is in the case. Did you still take the massless scale? I forget. 579 01:09:39,200 --> 01:09:50,740 Patricia Ribes Metidieri: So let's say that them Yes, we took the 580 01:09:50,870 --> 01:09:56,460 Patricia Ribes Metidieri: and then the way we need. The calculation was basically by introducing a small amount and then taking it to Z. 581 01:09:56,830 --> 01:10:07,290 Patricia Ribes Metidieri: Yes, because 1 one to similar location. And that's why I meant that the is actually finite in this, in me, even in the 582 01:10:07,430 --> 01:10:11,850 Patricia Ribes Metidieri: and it's that's what we are introducing a small. 583 01:10:20,200 --> 01:10:26,100 Abhay Vasant Ashtekar: So so the results are there also in the massive case is what I understood it. 584 01:10:26,190 --> 01:10:28,590 Abhay Vasant Ashtekar: Same resource holding a massive 585 01:10:28,930 --> 01:10:32,120 Patricia Ribes Metidieri: exactly same. 586 01:10:33,310 --> 01:10:34,210 Suddhasattwa Brahma: Okay. 587 01:10:41,150 --> 01:10:43,070 Jorge Pullin: I'll be able to thank the speaker again. 588 01:10:47,680 --> 01:10:48,120 Patricia Ribes Metidieri: Thank you.