Jorge Pullin: Okay. So our speaker today is Patricia Rivas met Theiri, who will speak about how ubiquitous is entanglement. And Kirsty.
Patricia Ribes Metidieri: Okay? Well, first of all. Thank you very much for giving me the opportunity to talk here today.
Patricia Ribes Metidieri: The work i'm going to present is a work that I've done, together with my Bhd.
Patricia Ribes Metidieri: And also we do wonderful collaborate to some friends, and they meet recently.
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.
Patricia Ribes Metidieri: So yeah, and that's I will just tell you what this talk is to me about.
Patricia Ribes Metidieri: I think
Patricia Ribes Metidieri: so. I will first talk what? Give a brief motivation for the topic I'm going to talk about Basically, in.
Patricia Ribes Metidieri: Then I will give you some details of how do we compute and time, I will present some results.
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
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
Patricia Ribes Metidieri: so let's consider. Please scale up in
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.
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.
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.
Patricia Ribes Metidieri: where this State, he says, the negotiations
Patricia Ribes Metidieri: are sufficient to generate the
Patricia Ribes Metidieri: what is not so incredibly reasonable, and it's the content of the recently the theorem
Patricia Ribes Metidieri: is that we can still generate the full in the space of the theory
Patricia Ribes Metidieri: with states of this form.
Patricia Ribes Metidieri: Even if we restrict all these functions to be supported in an arbitrarily small region of space time.
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.
Patricia Ribes Metidieri: So just let's say a picture experiment on my experiment.
Patricia Ribes Metidieri: Let's assume that we have one from laboratory here on it.
Patricia Ribes Metidieri: so that that can generate any one to operator. that we' not necessarily unitary operator, so you can generate whatever.
Patricia Ribes Metidieri: as long as these operators we are generating are contain within this one. and let's part that assume
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
Patricia Ribes Metidieri: one they.
Patricia Ribes Metidieri: my acting
Patricia Ribes Metidieri: on the on the vacuum state
Patricia Ribes Metidieri: with an operator that I
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
Patricia Ribes Metidieri: in one to mechanics.
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.
Patricia Ribes Metidieri: Oh, they mentioned in both of them.
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.
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.
Patricia Ribes Metidieri: If on this coefficients I I
Patricia Ribes Metidieri: then the steep side is called a fully and download state.
Patricia Ribes Metidieri: What if i'm mentioning on this is because we know that if I is a point in time of state.
Patricia Ribes Metidieri: then any state in the full delivery space on the hearing can be written in this form where this oh, okay.
Patricia Ribes Metidieri: it's an operator acting in.
Patricia Ribes Metidieri: and this is the identity operator in the space we.
Patricia Ribes Metidieri: And if you look at this one, you know it seems similar to the content of the
Patricia Ribes Metidieri: if we consider that this, but that all the days of freedom within the pantom that I was telling you about.
Patricia Ribes Metidieri: Basically, they did this a freedom of system, a and the rest of the
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
Patricia Ribes Metidieri: is that in content in theory, the vacuum stay
Patricia Ribes Metidieri: has already a very rich and dominant structure.
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.
Patricia Ribes Metidieri: In these calculations Basically, we take.
Patricia Ribes Metidieri: as I put these lines in our space. Them we select compact region of these lines.
Patricia Ribes Metidieri: and then we try to compute, and then we can communicate to them within this region and each
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.
Patricia Ribes Metidieri: and we know that it's not just that it's basically in.
Patricia Ribes Metidieri: So another important thing that I would like to mention is that
Patricia Ribes Metidieri: both these results that I've mentioned. So the reason that the them
Patricia Ribes Metidieri: and the calculations of
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.
Patricia Ribes Metidieri: I'm going to? I mean by in that. when
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.
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.
Patricia Ribes Metidieri: We often look at quantum fields.
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.
Patricia Ribes Metidieri: So that's the best. This in this picture that I have depicted here in the computer
Patricia Ribes Metidieri: is where we kind of can extract out of this one to.
Patricia Ribes Metidieri: So basically a final number of smear the list of freedom that our detectors can measure
Patricia Ribes Metidieri: what all this
Patricia Ribes Metidieri: It is also when none of the entertainment is not a property of quantum states alone.
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.
Patricia Ribes Metidieri: So the question that I would try to answer in this talk is whether there is an amendment
Patricia Ribes Metidieri: between these kind of systems that are motivated from expanding. As I I showed you this people.
Patricia Ribes Metidieri: which are then the system that I want to call in a way. Not
Patricia Ribes Metidieri: so. Before proceeding to that, let me tell you what a choice of these subsystems would be.
Patricia Ribes Metidieri: For where, I said, how how can we extract a single video freedom
Patricia Ribes Metidieri: out of the?
Patricia Ribes Metidieri: And again, we will do this through this meeting.
Patricia Ribes Metidieri: So let's take a for space them and let's select a region of
Patricia Ribes Metidieri: and from this region I will take as many function. Okay.
Patricia Ribes Metidieri: which, if you want, we can understand as the sensitivity of a one single detect.
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.
Patricia Ribes Metidieri: which are operators, smear in space with this is main function, and
Patricia Ribes Metidieri: also for convenience, I will choose this function it to be normalized, since that these operators are
Patricia Ribes Metidieri: one. So this defines a system with one.
Patricia Ribes Metidieri: and we can also define likewise.
Patricia Ribes Metidieri: So for
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
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
Patricia Ribes Metidieri: in which I'm. Going to to.
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.
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
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
Abhay Vasant Ashtekar: in Kansas City space. Yeah, that free, it feels important because you are doing space like wearing.
Patricia Ribes Metidieri: Yeah, yeah, Exactly. So they I think.
Patricia Ribes Metidieri: Yeah, this was he. Didn't: I mentioned it.
Abhay Vasant Ashtekar: Okay.
Patricia Ribes Metidieri: Okay. So
Patricia Ribes Metidieri: so how do we in this case?
Patricia Ribes Metidieri: One let's go back to the system with one degree of freedom.
Simone SPEZIALE: Another clarification is.
Simone SPEZIALE: and
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
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
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.
Simone SPEZIALE: But then you also have you find some lattice structure? Maybe?
Patricia Ribes Metidieri: Yes, exactly.
Patricia Ribes Metidieri: And
Simone SPEZIALE: the same degree of freedom many times, I suppose.
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.
Patricia Ribes Metidieri: and the whether or not they are independent will depend on the function of meeting that I'm. Using right
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:
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
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
Patricia Ribes Metidieri: explain needed
Patricia Ribes Metidieri: our general features that we have for let's say you all these many passes without that.
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.
Patricia Ribes Metidieri: We've also considered an independent. This support in the same region.
Patricia Ribes Metidieri: and the reasons we are going to present are basically well, let's say qualitatively the same.
Patricia Ribes Metidieri: And it's that one to find a number of let's say it.
Simone SPEZIALE: Thank you.
Patricia Ribes Metidieri: Yeah. What? Yeah. Yeah. Okay.
Patricia Ribes Metidieri: So yeah, sorry about that. Back to the system with a single degree of freedom.
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.
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.
Patricia Ribes Metidieri: which means, in particular that they reduce that city matrix representing this and these subsystems.
Patricia Ribes Metidieri: Yeah, that me, it can only be described by the go by its covariance.
Patricia Ribes Metidieri: which is basically
Patricia Ribes Metidieri: a matrix containing the the
Patricia Ribes Metidieri: 2 point functions. Once me at the Point functions.
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
Patricia Ribes Metidieri: Simon I was asking, because that is in a sense equivalent to a
Patricia Ribes Metidieri: where we do not select the degrees of freedom in advance. We basically take this
Patricia Ribes Metidieri: no way also. And then I'm going to stretch it over with you
Patricia Ribes Metidieri: and one in the they. The nice thing about this strategy as well is that
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
Patricia Ribes Metidieri: to this. The dependence, however, is that all the reduced States, coming from a quantity theory, are mixed
Patricia Ribes Metidieri: so that we cannot use the well they were not, and use for them an entropy
Patricia Ribes Metidieri: to measure, and
Patricia Ribes Metidieri: we wouldn't use instead.
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.
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,
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
Patricia Ribes Metidieri: positive.
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.
Patricia Ribes Metidieri: So for a system within a modes plus can be.
Patricia Ribes Metidieri: You can compute the
Patricia Ribes Metidieri: where these, where these contexts here have nothing else than the syntactic eigenvalues of the
Patricia Ribes Metidieri: So this object and will this
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
Patricia Ribes Metidieri: is that
Patricia Ribes Metidieri: if at least one of these is
Patricia Ribes Metidieri: but also, if we are interested in the activity is because it has a nice physical interpretation.
Patricia Ribes Metidieri: Basically, it is an
Patricia Ribes Metidieri: so how much entanglement we can extract of a system via local operations and classical communication
Patricia Ribes Metidieri: and production states it does, has the meaning as they entitlement post.
Patricia Ribes Metidieri: So how many bell pairs we would need to be able to create, or
Patricia Ribes Metidieri: it is Sigma Tilde, I'm. Confused. So can you go back to that last last slide, please?
Abhay Vasant Ashtekar: So it's. Yeah, no, no, not the one that you are. Yeah.
Abhay Vasant Ashtekar: Yeah, that one. So Sigma is a
Abhay Vasant Ashtekar: It's just a 2 by 2 matrix, or
Abhay Vasant Ashtekar: but is it just 2 by 2, or you? I got
Abhay Vasant Ashtekar: and a and Lb are running, or many
Abhay Vasant Ashtekar: one to a 120. Right? So Sigma is what
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
Patricia Ribes Metidieri: in particular.
Abhay Vasant Ashtekar: Okay. So I don't understand. The formula for t team is supposed to be.
Abhay Vasant Ashtekar: This is not a tensor product. It is a direct sum.
Patricia Ribes Metidieri: Yeah, this is.
Abhay Vasant Ashtekar: And so
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
Abhay Vasant Ashtekar: 2 in by 2 and a large number of
Abhay Vasant Ashtekar: dimensional back to space.
Abhay Vasant Ashtekar: Yes.
Patricia Ribes Metidieri: Well, basically. This
Patricia Ribes Metidieri: well, this matrix is just basically doing the same thing as taking the.
Patricia Ribes Metidieri: And in this case, maybe I should have mentioned that this is the 2 by 2 in the image.
Patricia Ribes Metidieri: and i'm partially transparent, and the the last can be degrees of freedom if you want.
Patricia Ribes Metidieri: So i'm just taking the pass at this position with respect to end meeting the Supreme
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
Patricia Ribes Metidieri: So this is just so. Let's say that for me these convenience meetings
Patricia Ribes Metidieri: is the one the the symmetries.
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
Patricia Ribes Metidieri: Yes, yeah.
Patricia Ribes Metidieri: okay. Is that the you know
Doyeon Kim: I have a question
Doyeon Kim: so why the von Neumann the enter cannot be quantified in this case to explain the part
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.
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
Patricia Ribes Metidieri: of this sort
Patricia Ribes Metidieri: they are mixed. As long as I understand
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.
Patricia Ribes Metidieri: And I thought, that is, that we define a number of
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.
Patricia Ribes Metidieri: Does this answer your question?
Doyeon Kim: Okay. Thank you so much.
Patricia Ribes Metidieri: I 2 of them.
Deepak Vaid: Can. I just follow up on that really quickly, because
Deepak Vaid: you can define the one number and entropy for any density matrix, right? I mean, you just have to choose.
Patricia Ribes Metidieri: Yeah, you can. Another thing is whether this density, this one i'm an entity has the meaning of an
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
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
Deepak Vaid: right, because they the
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
Patricia Ribes Metidieri: all the correlations coming from the mixedness and to the
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.
Patricia Ribes Metidieri: Yes, exactly.
Deepak Vaid: Thank you.
Patricia Ribes Metidieri: Yeah.
Patricia Ribes Metidieri: Okay. So yes, as I
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.
Patricia Ribes Metidieri: But i'm going to present i'm the
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.
Patricia Ribes Metidieri: where this
Patricia Ribes Metidieri: such that well depending on this parameter, that I mean different shapes of these sweating functions.
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
Patricia Ribes Metidieri: in the equal or larger than 2, as I will mention. I see
Abhay Vasant Ashtekar: this is a technical point, right? I Your Your
Patricia Ribes Metidieri: yeah. This functions are
Patricia Ribes Metidieri: is also linked to the differential ability class of these functions.
Patricia Ribes Metidieri: But yeah, let's see that we also discussed that the the fact that these pensions are not smooth is.
Patricia Ribes Metidieri: let's say not.
Ivan Agullo: And you also have results for smooth functions. Right?
Patricia Ribes Metidieri: Yes, we also have a so. Yeah, that's what i'm going to present
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
Patricia Ribes Metidieri: that then they.
Patricia Ribes Metidieri: the lack of smoothness of this particular functions is not a problem, or let's say it doesn't change our
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.
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.
Patricia Ribes Metidieri: and second, but it becomes harder and harder to finally. with increasing number of dimensions of space. And I mentioned.
Patricia Ribes Metidieri: So that's what I would like to present this. This results for different dimensions. First for the by one
Patricia Ribes Metidieri: we're basically the regions. I'm. Going to consider. I Just 9 s
Patricia Ribes Metidieri: of half men are separated by this distance. Drop in units of the radius with this hotline.
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
Patricia Ribes Metidieri: in explaining them.
Patricia Ribes Metidieri: But then I will present some populations in the
Patricia Ribes Metidieri: and finally also in the
Patricia Ribes Metidieri: and, as you already mentioned, the for one is a bit special, because, yeah, we cannot really
Patricia Ribes Metidieri: right the
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.
Patricia Ribes Metidieri: But the nice thing is that for whatever it of it
Patricia Ribes Metidieri: we have.
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.
Patricia Ribes Metidieri: And what we notice is that again, when this distance between the 2 regions is small.
Patricia Ribes Metidieri: This close correlations depend on the details of this meeting function.
Patricia Ribes Metidieri: But when this system here this distance grows, then we recover
Patricia Ribes Metidieri: the results we were expecting. So they then they gave him. We were expecting 48.1
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
Patricia Ribes Metidieri: which decay, as we expected for this dimensionality as one over the distance.
Patricia Ribes Metidieri: So once we did this, we would finally go and compute an element.
Patricia Ribes Metidieri: And this is one of the things
Patricia Ribes Metidieri: so in this part. What you can see is the
Patricia Ribes Metidieri: as a function of the the mass of the
Patricia Ribes Metidieri: when this, a new parameter is basically the mass in units of this, of the radius of the 2 segments.
Patricia Ribes Metidieri: and this is when the 2 segments are almost touching each other. So at the distance for almost able to do.
Patricia Ribes Metidieri: and there are a couple of things that are in what mentioned.
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.
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.
Patricia Ribes Metidieri: and near the boundary of this section of this region here.
Patricia Ribes Metidieri: and they they are better in. The The second thing we notice is that well, when the mask is sufficiently small.
Patricia Ribes Metidieri: this and that is basically what which is a plateau. But as the the this is very rapidly
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.
Patricia Ribes Metidieri: The second thing we we try to compute is, what is the behavior of the
Patricia Ribes Metidieri: as a function of the separation of the 2 regions we are for a fixed.
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.
Patricia Ribes Metidieri: in fact, within a 2025% of the radius, it completely doesn't in the best.
Patricia Ribes Metidieri: Then we have something
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.
Patricia Ribes Metidieri: And
Patricia Ribes Metidieri: and once again we just check the that the press correlations between the we had, as one would expect for the
Patricia Ribes Metidieri: and the symbols for them open information. We also they forward the expected for them. We, even
Patricia Ribes Metidieri: for any of this meeting functions that I just showed.
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.
Patricia Ribes Metidieri: But okay, this is just a him. So then we need the same thing. For the
Patricia Ribes Metidieri: once again we computed the they all the elements of the openings meetings
Patricia Ribes Metidieri: we take that the correlations between field and and decay is expected, and long distances the same for the information. The
Patricia Ribes Metidieri: but once again i'm sure you will not be too surprised when I tell you that we didn't.
Patricia Ribes Metidieri: And to be honest, this was kind of a surprise, and this was not the only form of
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
Patricia Ribes Metidieri: So we drive for the
Patricia Ribes Metidieri: I mean in those plots. It was not clear that it was actually 0, right? It was small
Abhay Vasant Ashtekar: for large values of a row. The entitlement, the login
Abhay Vasant Ashtekar: in those plots was, was it identically 0? I mean within numerical errors or
Abhay Vasant Ashtekar: so I'm. I'm. In between this to be the museum. But we thought that maybe
Abhay Vasant Ashtekar: for a large role it is
Abhay Vasant Ashtekar: for some value of row
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.
Patricia Ribes Metidieri: Technically, we should not get there but the
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.
Patricia Ribes Metidieri: So even in the optimal case, we did not find entertainment for any of these meeting functions, we
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.
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.
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
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
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
Ivan Agullo: Okay? So that was my question, because in the in the plots I was not.
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
Abhay Vasant Ashtekar: yeah.
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
Patricia Ribes Metidieri: This is a concerning D. 8 by one.
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.
Patricia Ribes Metidieri: But okay, this is still a many countries. The nice thing of the how many of functions that I was
Patricia Ribes Metidieri: using, as you pointed out.
Patricia Ribes Metidieri: is that in highly dimensions we have exact analytical populations. We can for good. Exactly how much is the the
Ivan Agullo: So can you go to the slide of of moodle information
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.
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.
Ivan Agullo: and Patricia has computed, in addition to this plot, entanglement, and entanglement is exactly 0.
Ivan Agullo: Therefore.
Ivan Agullo: this moodle information contains just the classical correlations that that's the point.
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
Abhay Vasant Ashtekar: know that analytically design integral is 0.
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.
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.
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?
Patricia Ribes Metidieri: Hmm. I think so. Yeah. I think it it would be possible and
Patricia Ribes Metidieri: sorry. Say it again.
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?
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
Patricia Ribes Metidieri: and what.
Patricia Ribes Metidieri: and then, you know, like we didn't find. But we didn't think it was so
Patricia Ribes Metidieri: let's say, yeah.
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.
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.
Patricia Ribes Metidieri: because in the end. And this when we see for this, this ring, function, system
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.
Abhay Vasant Ashtekar: Why do you think? Why do you think spherical symmetry has anything to do with anything? I mean
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.
Simone SPEZIALE: and whether the things could look different
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
Patricia Ribes Metidieri: in which we do manage to.
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
Patricia Ribes Metidieri: The main point of the talk is that you know, finding and time, and we find a dimension of systems.
Patricia Ribes Metidieri: It's not as easy as we thought it would be.
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.
Deepak Vaid: But yeah, there is one
Deepak Vaid: one question that what if You' what if you turn on interactions
Deepak Vaid: and you turn them on very, very slowly.
Deepak Vaid: And then I
Deepak Vaid: right? And the moment you turn interactions on
Patricia Ribes Metidieri: Yes.
Deepak Vaid: is it possible that that that no matter how week your interactions are, you certainly do develop in time moment.
Patricia Ribes Metidieri: Okay.
Patricia Ribes Metidieri: to be honest, I have not explored this, but all the results i'm presenting I just for
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
Patricia Ribes Metidieri: based.
Deepak Vaid: you you turn it on and
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.
Ivan Agullo: I mean.
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.
Ivan Agullo: And and it is accepted that you know the code of entanglement in one of the 30 is already included in
Ivan Agullo: in in the free theory.
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.
Ivan Agullo: But of course you know, checking it at the level of calculations is is very challenging.
Deepak Vaid: Yeah.
Deepak Vaid: Thanks.
Patricia Ribes Metidieri: Okay.
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.
Patricia Ribes Metidieri: and for the that, the strategy or not to be quite prolific. And we found several examples
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.
Patricia Ribes Metidieri: where we take to end the release of freedom. Then I'm: basically supported and completely supported within these seconds.
Patricia Ribes Metidieri: And we divide these
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
Patricia Ribes Metidieri: that contains all the needs of freedom supported in the Reds.
Patricia Ribes Metidieri: What the we find 2 things. The first one is that the enrollment in cases linearly
Patricia Ribes Metidieri: with the number of
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
Patricia Ribes Metidieri: in this particular example. The minimum number of these days of premium is 4, but that's a a particular example.
Patricia Ribes Metidieri: and our configuration that, I also think, is quite interesting. He's in
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
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
Patricia Ribes Metidieri: in this particular case.
Patricia Ribes Metidieri: But that, again, is a feature that depends on how this meeting actually.
Patricia Ribes Metidieri: and the other thing that we see that is, that is, that the entertainment Saturday week.
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?
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
Patricia Ribes Metidieri: with the
Patricia Ribes Metidieri: But
Patricia Ribes Metidieri: once again in the 3 dimensions. What we learned is that the environment is yeah, quite difficult to find.
Patricia Ribes Metidieri: and I can tell you that we drive of the order of 17 modes, but also
Patricia Ribes Metidieri: and also these kind of configurations, where we try to maximize the surface of contact between the 2 subsystem.
Patricia Ribes Metidieri: But as you were pointing out. This is also a consequence of type of regions of support, and what we are.
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.
Patricia Ribes Metidieri: But this is not the only thing we have tried, not at all.
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.
Patricia Ribes Metidieri: All the Prime Minister's main function, and also in the we are most defined within the same regions.
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
Patricia Ribes Metidieri: entanglement is in general and difficult to find. and it's more difficult to do this in dimensions.
Patricia Ribes Metidieri: Does this mean that there is no time? Not at all, absolutely not this, not what we are saying.
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
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?
Patricia Ribes Metidieri: And they find new sets of operators is a by one Brian, and by one
Patricia Ribes Metidieri: there are linear combinations of the operators they find properly supported in regions. K. And
Patricia Ribes Metidieri: this parameter R is often called the discreasing intensity, and one can show
Patricia Ribes Metidieri: that this subsystem, so the subsystems made of one. My, these things of freedom
Patricia Ribes Metidieri: I didn't tell you.
Patricia Ribes Metidieri: for all squeezing and density is larger than a.
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.
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
Patricia Ribes Metidieri: between what we call different subsystems. That would be something like this.
Patricia Ribes Metidieri: What we define a month here, this again spit it, and then we define other modes
Patricia Ribes Metidieri: in a.
Patricia Ribes Metidieri: and here it is we manage to.
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
Patricia Ribes Metidieri: What's that? A question?
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.
Patricia Ribes Metidieri: Yeah. Okay. So the same mentioned.
Veso: Yes, I I have a quick question.
Veso: Can you hear me?
Patricia Ribes Metidieri: Yes, yes, please go ahead.
Veso: So to to understand You're looking at 2.4, 2 point
Veso: function correlations.
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.
Veso: I mean, rather than using the vacuum.
Patricia Ribes Metidieri: as I mentioned at the beginning, and in this particular work we were interested in just looking at the.
Patricia Ribes Metidieri: and we did not try any any other things.
Patricia Ribes Metidieri: But I
Patricia Ribes Metidieri: basically.
Patricia Ribes Metidieri: And let's say that when
Patricia Ribes Metidieri: yeah, we didn't try other things. But I think
Patricia Ribes Metidieri: that the for other adoption states, for example, it will be.
Patricia Ribes Metidieri: The situation will be
Veso: okay
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
Patricia Ribes Metidieri: Let's see how this works.
Veso: Thank you.
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
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.
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.
Patricia Ribes Metidieri: and one of its nice predictions is that the density perturbations that in every universe set as seeds
Patricia Ribes Metidieri: for all this
Patricia Ribes Metidieri: in particular.
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
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
Patricia Ribes Metidieri: when they 2 days of freedom
Patricia Ribes Metidieri: close to the end of completion.
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.
Patricia Ribes Metidieri: and instead of looking at inflation, i'm going to
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.
Patricia Ribes Metidieri: and in the in the one's previous vacuum. I'm. Trying to compute a. And
Patricia Ribes Metidieri: And what we found is that even though there are no correlations in the
Patricia Ribes Metidieri: are fewer than these correlations contain in them.
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.
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.
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
Patricia Ribes Metidieri: for the is basically the quantity that the tenants what local activities, and or whether or not there is some time.
Patricia Ribes Metidieri: can we read them in this form
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.
Patricia Ribes Metidieri: An important point is that this function here is always positive for all values of distance
Patricia Ribes Metidieri: and for the
Patricia Ribes Metidieri: and yeah, this one which means in particular this
Patricia Ribes Metidieri: they
Patricia Ribes Metidieri: in
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
Abhay Vasant Ashtekar: the but the point about this the sitter or inflation would be to understand the time. Get timers right.
Abhay Vasant Ashtekar: In other words, maybe at some time there's been some entanglement, but
Abhay Vasant Ashtekar: what happens at later time, because the Milkowski space. Nothing changes in time, but here things do change in time.
Abhay Vasant Ashtekar: And so it seemed to me just quickly that, in fact, the entire entertainment even
Patricia Ribes Metidieri: reduces in time. Is that true or not?
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
Patricia Ribes Metidieri: and I'm. 3 as the inflation proceeds. So this radius from this physical distance goes.
Patricia Ribes Metidieri: and what becomes less likely this is that this.
Patricia Ribes Metidieri: Let them. Yeah. This.
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.
Abhay Vasant Ashtekar: because I can from it's conformity related to the in the case space. But this is a massive scale of
Abhay Vasant Ashtekar: it's probably related, and so the fall off with respect to the distance will be physical. Distance
Patricia Ribes Metidieri: is.
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?
Ivan Agullo: A. As as as Patricia nicely pointed out, because you know
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
Ivan Agullo: at super Hubble distances. The 2 point function goes to a constant given by the square of the Have a right.
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.
Ivan Agullo: and what, Patrice, your phone is the other way around.
Ivan Agullo: What is far better away
Ivan Agullo: from entanglement, although you know far away from 0, it is still 0,
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.
Abhay Vasant Ashtekar: Okay, we should discuss this later. But
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
Abhay Vasant Ashtekar: so. But maybe we should talk about That's the
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.
Patricia Ribes Metidieri: but it was more difficult to find it than we had expected, for a finite dimensional systems.
Patricia Ribes Metidieri: and this entertainment seems to be distributed in a certain way.
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.
Patricia Ribes Metidieri: or that we, if we want to find it, we have to select very carefully. We are using.
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.
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.
Patricia Ribes Metidieri: So yeah, that's that's one.
Patricia Ribes Metidieri: And I would like to thank you very much for your attention.
Patricia Ribes Metidieri: Yeah. And we happy to answer any questions that Haven't.
Jorge Pullin: Yeah, we are.
Adrià Delhom i Latorre: So thanks for for the nice talk.
Adrià Delhom i Latorre: I was wondering I don't know if it makes sense. But I was wondering how you tried to use
Adrià Delhom i Latorre: this meeting function is that somehow the article moving with the with the they also increase.
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.
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
Patricia Ribes Metidieri: but the second, the second piece
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
Patricia Ribes Metidieri: but when keeping them at the same, let's say at the same.
Adrià Delhom i Latorre: Okay. Okay, Thank you.
Patricia Ribes Metidieri: Cool.
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.
Patricia Ribes Metidieri: Yeah, that is correct.
Suddhasattwa Brahma: And are these 2 patches within the horizon, or like? Are they separated?
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.
Patricia Ribes Metidieri: and the point is that if if these regions are small and well contained within the Hubble radius. then the
Patricia Ribes Metidieri: well, we take these 2 patches to be much bigger than separated. What distances that are of the
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.
Patricia Ribes Metidieri: In a sense. For, as I mentioned, this is not a measurement of how far we are from. Okay.
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.
Suddhasattwa Brahma: And you're finding that it's actually getting
Suddhasattwa Brahma: smaller. Not larger.
Patricia Ribes Metidieri: Yes, please.
Jorge Pullin: Other questions.
Abhay Vasant Ashtekar: Maybe you can comments a little bit about your your understanding of why. as dimension increases.
Abhay Vasant Ashtekar: the enrollment becomes less and less.
Patricia Ribes Metidieri: Well, basically we know the correlations decrease faster.
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.
Patricia Ribes Metidieri: And in the case of this
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.
Patricia Ribes Metidieri: But i'm. And then, when we even more and we think the same space information.
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.
Abhay Vasant Ashtekar: Is there some intuitive understanding, eg. For example, that
Abhay Vasant Ashtekar: degrees of freedom have more room
Abhay Vasant Ashtekar: to be in time, but I mean, you know, in in the higher dimensions.
And so you're probing a given the
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.
Abhay Vasant Ashtekar: the main dependence on the dimension
Patricia Ribes Metidieri: Hmm.
Abhay Vasant Ashtekar: I mean it's more than the the fall of of the
Patricia Ribes Metidieri: Yes, yes, of course. And then the point is
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
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.
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.
Patricia Ribes Metidieri: But exactly how the let's see the
Abhay Vasant Ashtekar: I just had one small comment about it was about what I was asking about. Normally you talk about
Abhay Vasant Ashtekar: momentum modes and degrees of freedom in that way. To me at least, I mean that is.
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.
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
Abhay Vasant Ashtekar: what the Simone was
Abhay Vasant Ashtekar: proposing is an alternative, and I wonder if somebody has some comment on that
Simone SPEZIALE: I see. Well. that that's true. But then
Simone SPEZIALE: there's this finite size effect that it's a
Simone SPEZIALE: not clear to me yet how
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
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.
Abhay Vasant Ashtekar: But now you can run the same test.
Simone SPEZIALE: because they are partially overlapping. So that's the kind of a
Simone SPEZIALE: I I was thinking more of of this partial overlapping as a tricky aspect rather than going from a moment to
Abhay Vasant Ashtekar: Yeah. But in the moment in space it is complete overlap.
Simone SPEZIALE: Yes.
Abhay Vasant Ashtekar: I mean, and the the my, those are either my complete or like in space.
Abhay Vasant Ashtekar: That's right. I think that that is, I think
Abhay Vasant Ashtekar: I don't know.
Simone SPEZIALE: and so to keep going down design. So in the end
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
Patricia Ribes Metidieri: and
Simone SPEZIALE: sorry. Can you repeat the question
Simone SPEZIALE: in the end. Politically, they don't depend so much on these shape that you use.
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
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
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
Patricia Ribes Metidieri: it's. In principle it's easier to panel, as in the case of these spherical shs overlapping each other.
Patricia Ribes Metidieri: But still
Patricia Ribes Metidieri: What we expect is that you know we not any function or not in this many fashion.
Patricia Ribes Metidieri: I will give you
Patricia Ribes Metidieri: fine.
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.
Patricia Ribes Metidieri: We are in 3 dimensions, so I don't think it's going to.
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.
Patricia Ribes Metidieri: and that is again. That is just the process of.
Patricia Ribes Metidieri: and then you can find us with the squeezing that you want. But then the resulting
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.
Deepak Vaid: That's
Simone SPEZIALE: right.
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.
Simone SPEZIALE: But to understand the answer, thank you
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.
Patricia Ribes Metidieri: Yeah, thank you.
Jorge Pullin: Any other
Suddhasattwa Brahma: sorry one quick question which is in the case. Did you still take the massless scale? I forget.
Patricia Ribes Metidieri: So let's say that them Yes, we took the
Patricia Ribes Metidieri: and then the way we need. The calculation was basically by introducing a small amount and then taking it to Z.
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
Patricia Ribes Metidieri: and it's that's what we are introducing a small.
Abhay Vasant Ashtekar: So so the results are there also in the massive case is what I understood it.
Abhay Vasant Ashtekar: Same resource holding a massive
Patricia Ribes Metidieri: exactly same.
Suddhasattwa Brahma: Okay.
Jorge Pullin: I'll be able to thank the speaker again.
Patricia Ribes Metidieri: Thank you.