1 00:00:03,010 --> 00:00:07,090 Thank you very much for the introduction. Can you can hear the book? Is it okay? 2 00:00:07,510 --> 00:00:10,780 Yes. Great. So, yeah. 3 00:00:10,780 --> 00:00:15,420 So this talk will be about story mostly. So it's an interesting story. 4 00:00:15,430 --> 00:00:22,630 So a story of quantum information, a small thread that went happen at some point. 5 00:00:23,590 --> 00:00:29,950 But we start with a very basic point, which is thanks to quantum physics, 6 00:00:30,100 --> 00:00:38,800 we all have learned at some point this statement in a way or another that the outcomes of a measurement do not exist. 7 00:00:39,340 --> 00:00:47,080 The measurement. This is one of the. Things that we learn to believe when we start studying quantum mechanics. 8 00:00:47,830 --> 00:00:52,060 And if you think, where's this been proved? 9 00:00:52,300 --> 00:00:58,430 Where does this come from? Probably in the traditional way of teaching quantum mechanics. 10 00:00:58,430 --> 00:01:03,139 The answer would be Heisenberg saying that the relations right, 11 00:01:03,140 --> 00:01:11,040 because there is the first case where explicitly it was noticed that not all physical observables can have sharp values. 12 00:01:11,060 --> 00:01:17,540 If I know the value of the if I if the state is such that the value of the valuable position is well known, 13 00:01:17,810 --> 00:01:21,770 it turns out that the variable momentum is not so well-defined. 14 00:01:22,370 --> 00:01:27,439 And which means that if I measure momentum, a negative result where this outcome did not exist. 15 00:01:27,440 --> 00:01:37,559 My measurement. Now. In order to introduce inequalities, I want to somehow criticise and sovereignty relations. 16 00:01:37,560 --> 00:01:43,170 My criticise no. But Bush explained that they don't have some features that we would like to have. 17 00:01:43,470 --> 00:01:47,010 Especially you think of trying to convince someone who doesn't believe in that statement. 18 00:01:47,820 --> 00:01:51,240 That is, after all, a pretty strong statement. So what happens with 71 nations? 19 00:01:51,630 --> 00:01:55,680 First of all, they could be interpreted. It's not the orthodox way. 20 00:01:56,340 --> 00:02:03,479 I hope your teachers have told you not to do that, but they could be interpreted as imperfections of our measurement devices. 21 00:02:03,480 --> 00:02:07,830 And it turns out, as you probably know, Heisenberg himself made that mistake. 22 00:02:08,880 --> 00:02:12,120 So after driving correctly, mathematically, he's on 70 relations. 23 00:02:12,120 --> 00:02:15,120 When asked in a Sydney popular book to explain what happens. 24 00:02:15,540 --> 00:02:18,500 He came up with this idea of the microscope where, you know, 25 00:02:18,540 --> 00:02:23,219 there is the particle coming there and then in order to measure it, they must interact with a photon. 26 00:02:23,220 --> 00:02:26,730 And a photon is almost each barber calculation. 27 00:02:26,730 --> 00:02:33,420 Something comes out and then a semi classical model for that, which is not wrong, but it doesn't capture the whole yet the whole idea. 28 00:02:34,080 --> 00:02:39,090 Besides, I can easily falsify an uncertainty relation with crappy measurements. 29 00:02:39,630 --> 00:02:42,780 Imagine that my measurement of position I don't plug it in. 30 00:02:43,320 --> 00:02:46,980 And so the needle is stuck there at zero. I did. 31 00:02:47,010 --> 00:02:52,170 You know, I get that x equals zero. Violating the uncertainty relations. 32 00:02:52,380 --> 00:02:54,720 They always say, Oh, but this is a bad measurement of how you check it. 33 00:02:56,640 --> 00:03:03,720 So you need to have perfect measurements, even perfectly well-characterized in order to test and uncertainty relation. 34 00:03:04,700 --> 00:03:10,429 And I can again. I can easily fool you by selling you and calibrate the device so badly. 35 00:03:10,430 --> 00:03:14,270 Can you buy the device that would convince you to do something which you actually do not hold? 36 00:03:14,270 --> 00:03:23,610 And I can measure position and momentum perfectly. So in fact, the conclusive test that the outcomes not exist is these violation of inequalities. 37 00:03:25,620 --> 00:03:30,240 I'm sorry if I don't even write down in the whole talk a single inequality. 38 00:03:31,260 --> 00:03:34,770 To understand this talk, you don't need to have the equation and the inequality. 39 00:03:34,770 --> 00:03:41,160 It's an inequality, something smaller than something else. But I would not spend time describing what it is. 40 00:03:41,430 --> 00:03:45,480 You have to believe me in these. Most of you probably have heard these things before anyway. 41 00:03:46,290 --> 00:03:49,860 So what happens with inequality is, first of all, you cannot fake it experimentally. 42 00:03:49,890 --> 00:03:53,610 So if you have a bad measurement, you may end up not violating the inequality. 43 00:03:53,610 --> 00:03:58,080 But if you do violate somehow is a simplification that things are going pretty well. 44 00:03:59,850 --> 00:04:05,520 Contractually on seventh in relation. Now it's a is a statement that these things are independent. 45 00:04:05,520 --> 00:04:08,560 So the inequality itself does not rely on quantum theory. 46 00:04:08,580 --> 00:04:13,049 I'm not gonna tell you again to yourself that the relations for which I need the formalism 47 00:04:13,050 --> 00:04:18,480 of quantum theory in order to then verify that indeed this to operate does not compute. 48 00:04:18,480 --> 00:04:21,570 And they have all these various relationships. 49 00:04:23,380 --> 00:04:28,000 It's something that you really write down. What does it mean that the results pre exist? 50 00:04:28,780 --> 00:04:32,139 And this implies some conditions and that's what you write down. 51 00:04:32,140 --> 00:04:36,850 And then you test that in the lab or in quantum theory, these conditions may not be satisfied. 52 00:04:36,850 --> 00:04:44,009 That can be violated. A consequence of these on which I will come back a lot is that this device independent? 53 00:04:44,010 --> 00:04:48,570 This means that it does not rely on a description of what is being measured. 54 00:04:49,640 --> 00:04:58,040 So it doesn't matter if I'm measuring photons, I'm measuring atoms and measuring Bose-Einstein condensates, electrons in solids, whatever system. 55 00:04:59,410 --> 00:05:01,330 The inequality does not depend on that. 56 00:05:01,540 --> 00:05:10,350 So the the assessment that the benefit what is being violated does not depend on my knowledge of the experiences. 57 00:05:10,540 --> 00:05:15,190 Needless to say, the experimentalist always doing the thing as better know their job. 58 00:05:16,150 --> 00:05:19,330 So the experimentally should know that they are dealing with photons and measuring polarisation. 59 00:05:19,330 --> 00:05:23,850 They should do it very, very well. But myself, as a verifier, I don't need any of this knowledge. 60 00:05:23,860 --> 00:05:29,890 I just can look at statistics and say, Oh yeah, this phenomenon, whatever it is, by all these bad inequalities. 61 00:05:30,940 --> 00:05:35,320 It got very exciting because I've be first noticed by John Bell in 1964. 62 00:05:36,220 --> 00:05:41,080 So more than 50 years ago and have been many experiments with what John Bell 63 00:05:41,080 --> 00:05:45,459 noticed is that the predictions of quantum theory are incompatible with that. 64 00:05:45,460 --> 00:05:49,230 Of course, at the end of the day, the jury is out and the jury's nature, 65 00:05:49,240 --> 00:05:57,310 you have to ask nature whether quantum theory is correct or is close to correct, gives the right prediction in these cases, or maybe not. 66 00:05:57,550 --> 00:06:03,190 And if both had been made and all of them easily came very close to the predictions of quantum theory. 67 00:06:04,330 --> 00:06:09,490 The first one that is considered conclusive is 1982 by Alan Spain near Paris. 68 00:06:10,210 --> 00:06:20,350 And you might know that two years ago, one year and a half ago, three groups reported three allegedly loophole free bell tests, whatever that means. 69 00:06:20,350 --> 00:06:24,790 We can enter into these technical details later. There were some loopholes. 70 00:06:24,790 --> 00:06:30,250 I mean, if you are really a crackpot, you could think that there were some loopholes in the experiments of us being other people. 71 00:06:32,350 --> 00:06:35,770 You really need to think carefully. But yeah. So anyway, 72 00:06:35,770 --> 00:06:40,380 this loophole free had been made in Delft in Vienna and well with a source and 73 00:06:40,900 --> 00:06:44,320 optics based in Neath and then with plenty of collaborators around the world. 74 00:06:46,990 --> 00:06:52,720 Now, as I said, measurements do not reveal a pre-existing property is a pretty strong statement. 75 00:06:53,800 --> 00:06:57,880 In fact, as a student, at least you and I should have questioned it. 76 00:06:58,940 --> 00:07:02,990 Well, normally we don't we just accept we have to pass the exam, right? So you better repeat it. 77 00:07:03,860 --> 00:07:10,400 But it has been. It is to get some. Debates some confusions. 78 00:07:10,910 --> 00:07:14,690 Some people have been speaking of local variables. 79 00:07:15,590 --> 00:07:18,800 It's not the way he done is not the way local. What does he mean local? 80 00:07:19,040 --> 00:07:23,750 Some people get very, very angry if you say that quantum theory is non-local because quantum theory is local. 81 00:07:23,900 --> 00:07:28,010 Of course, these different definitions and they just like to entertain the discussion 82 00:07:28,190 --> 00:07:34,220 instead of clarifying the definition and knowing that there's no discussion. But, you know, things happen anyway from the youngest among us. 83 00:07:35,210 --> 00:07:43,820 Probably this is a very constructive kind of discussion compared to what we might have had, which something of this type. 84 00:07:46,480 --> 00:07:52,700 But I made up these ones. 85 00:07:54,000 --> 00:07:58,700 But nobody cares at this point. Right? So whether it's authentic or not is no longer a question. 86 00:08:01,370 --> 00:08:06,889 So anyway, so that's the situation of quantum theory around the 1980s that yeah, 87 00:08:06,890 --> 00:08:11,150 there are plenty of, let's call them conceptual problems or things that are a bit troubling. 88 00:08:12,200 --> 00:08:16,189 The measurements modify the state. The realism is no longer there. 89 00:08:16,190 --> 00:08:20,839 Yeah, whatever. And then, well, you know, this quantum theory is fantastic. 90 00:08:20,840 --> 00:08:29,030 So you can just go ahead by not listening to all these problems and calculating things and you get always the right predictions. 91 00:08:30,230 --> 00:08:35,390 And somehow I like to think that quantum information is like the guy in the middle of you recognise who he is, 92 00:08:35,900 --> 00:08:40,129 who decided to not to give in to the song of the sirens. 93 00:08:40,130 --> 00:08:45,410 Not by not listening, but by listening, but being forced not to follow them. 94 00:08:45,530 --> 00:08:50,329 And because otherwise, you know, what's called the the mythology goes that if you listen to them and you are free to go, 95 00:08:50,330 --> 00:08:53,930 then you would automatically go and jump in the sea. 96 00:08:54,530 --> 00:08:58,640 So the question that the quantum information community started asking is, 97 00:08:59,180 --> 00:09:04,070 can all these we have stuff be actually useful for something given that it's there? 98 00:09:06,390 --> 00:09:15,330 And. Well, I'll give you the first example where some of these real quantum stuff as it is 99 00:09:15,330 --> 00:09:21,150 itself was identified as useful is quantum key distribution of quantum cryptography. 100 00:09:21,180 --> 00:09:27,480 Let me remind you what that is. That's the scheme of Benetton Brussel in 1984. 101 00:09:28,770 --> 00:09:32,040 The idea is to distribute between two partners, Alice and Bob. 102 00:09:32,040 --> 00:09:44,400 All good people. Secret key at a distance so that later they can exchange secret messages by encoding these messages to the secret code. 103 00:09:44,430 --> 00:09:49,290 So the idea that is, of course, everybody's been exchanging secret codes for many years. 104 00:09:49,320 --> 00:09:55,740 The idea here is to do it at a distance, because otherwise, if I'm lucky, I can also go to LA to give him my piece of paper. 105 00:09:56,130 --> 00:10:02,640 He keeps it and we have done it. But the idea is that I don't want to come closer to him at a distance connected by some channel. 106 00:10:03,510 --> 00:10:14,370 And then one of them got some notice that if Alice prepares a speech in half in four possible states, plus z minus that plus x minus six. 107 00:10:16,080 --> 00:10:19,940 And Bob measures the Z based on the X basis. 108 00:10:19,950 --> 00:10:29,130 What happens? Well, it's pretty clear what that means, right. So if if we are placid and Bob measures said he would get plus minus Z minus. 109 00:10:29,400 --> 00:10:35,280 But if Bob measures Z but at least we build something like X in the complementary bases. 110 00:10:35,280 --> 00:10:38,190 The results are completely random because again, they don't exist. 111 00:10:38,880 --> 00:10:46,260 So the if the state specifies the direct, the speeding the direction X in the direction Z is completely randomised. 112 00:10:46,860 --> 00:10:52,350 And similarly, of course symmetrically, I'm not going to tell you how the scheme goes about in creating. 113 00:10:52,620 --> 00:10:57,240 Well, essentially you see that the idea here is that now if they've measuring the same basis, 114 00:10:57,930 --> 00:11:05,050 if the measurement and the point based on the same basis, then Alison both share the same at least has kept the plus. 115 00:11:05,070 --> 00:11:08,430 And Bob has discovered a plus or minus and a minus. 116 00:11:08,820 --> 00:11:11,670 And if they measure in different bases, they can describe them later. 117 00:11:13,690 --> 00:11:22,629 And the idea here is that measurement modifies the state is put to the fruition by thinking that it's an annoyance. 118 00:11:22,630 --> 00:11:30,430 It's an annoyance, yes, but for the enemy. So the eavesdropper theory called evil is there in the middle trying to learn because 119 00:11:30,430 --> 00:11:35,560 she would like to share the secret in order to decrypt the secret communication symbol. 120 00:11:36,100 --> 00:11:40,650 But if Eve tries to measure what happens here, she modifies the state. 121 00:11:40,660 --> 00:11:43,720 What does it mean? It means that this that these things will no longer be seen. 122 00:11:45,010 --> 00:11:48,450 And I stumbled by checking some of their results. 123 00:11:48,460 --> 00:11:52,660 They could see that there was a problem in the middle. We don't have the perfect statistics. 124 00:11:52,690 --> 00:11:56,490 We have some noise there. Someone may be on the line. 125 00:11:56,510 --> 00:12:02,360 Let's stop the communication. So that's the idea how the idea of measurement modifies the state. 126 00:12:02,360 --> 00:12:10,640 One of these quantum we of NASA's whatever to call it is put to fruition in order to guarantee security against sort of. 127 00:12:12,570 --> 00:12:19,320 Now here comes one. By the way, I should have said at the beginning that the talk I'm going to give also involves many people that, 128 00:12:19,980 --> 00:12:23,380 uh, you may know and some of them even in the room. 129 00:12:23,730 --> 00:12:32,250 And in fact, the next one I have to mention is Autoworker Walker, who in 1991 rediscovered the idea of quantum solutions, which is the same. 130 00:12:33,520 --> 00:12:39,140 Sharing a secret key between two partners but using now entanglement. 131 00:12:39,160 --> 00:12:43,330 So using these outcomes not pre-existing that they associated to inequalities. 132 00:12:44,960 --> 00:12:49,340 I think I can do better than just reading what Atwater wrote in the paper. 133 00:12:50,400 --> 00:12:57,740 You see, the eavesdropper cannot elicit any information from the particles while in transit from the source to the legitimate users, 134 00:12:58,010 --> 00:13:02,720 simply because there is no information encoded there. The results do not pre-existed the measurement. 135 00:13:04,670 --> 00:13:13,569 Then the information comes into being only after whatever noticed that at the time that you've stopped it will still a man later go to work on Eve. 136 00:13:13,570 --> 00:13:18,310 But nowadays, probably they all should say they write something that is safer and inclusive. 137 00:13:19,720 --> 00:13:23,110 So you may say, Oh, fine, let's finish the talk here. 138 00:13:23,650 --> 00:13:29,140 We have an application for this strange idea that outcomes do not exist. 139 00:13:30,190 --> 00:13:35,320 It's helpful for key distribution, and he always gets complicated. 140 00:13:36,500 --> 00:13:44,660 Because. The following year, the same two guys as before Bennett and Bass, plus David Mermin, probably well known to some of you, 141 00:13:45,090 --> 00:13:53,729 were known in physics, teamed up to stress that the protocol of EQ is essentially the same as the B. 142 00:13:53,730 --> 00:13:57,210 The 84 protocol is a sort of the entanglement based version, 143 00:13:57,600 --> 00:14:03,510 and the idea is somehow the following if you consider that all these things belongs to Alice. 144 00:14:05,390 --> 00:14:08,100 Then. Well, trust me if you don't. 145 00:14:08,120 --> 00:14:17,630 But this is not it's not that difficult to prove that the produced to entangle pairs and least measures one in the ex based on the Z basis. 146 00:14:18,170 --> 00:14:25,100 What happens? Well, she gets the result and automatically the photon that goes to Bob gets split up in the same state. 147 00:14:26,790 --> 00:14:32,190 Okay. So somehow you can consider that this thing is the source of Alice. 148 00:14:32,640 --> 00:14:42,210 The only difference being that in the novel Dignity for All, Alice actively has to choose the basis or in fact, the state he it's chosen. 149 00:14:43,020 --> 00:14:47,069 She can choose the basis, and then the state is chosen at random by the quantum system. 150 00:14:47,070 --> 00:14:53,820 But it's exactly the same. And indeed, if you look at the correlations, the conditions are the same. 151 00:14:54,330 --> 00:15:01,230 So if both Measure Z, they get either both plus or both minus. 152 00:15:02,130 --> 00:15:05,630 If both Measure X, they get either both plus or both minus. 153 00:15:05,640 --> 00:15:12,850 If they measure in different bases, they get random things. So it seems that. 154 00:15:13,970 --> 00:15:17,360 This idea. Somehow the idea of outcome do not exist. 155 00:15:17,360 --> 00:15:27,170 Yeah, it's useful. But you get diluted into the into the same scheme as measure and modifies the state and then well whatever. 156 00:15:28,160 --> 00:15:33,590 Let me go be for wanting theoretical quantum redistribution because these ideas have been very, very influential. 157 00:15:33,590 --> 00:15:34,310 In particular, 158 00:15:35,990 --> 00:15:44,470 the dis translation between entanglement based and preparing measure schemes have been the key to what is called the proof of unconditional security. 159 00:15:44,630 --> 00:15:48,140 This is a technical world. Don't take me to face value is not is unconditional. 160 00:15:48,140 --> 00:15:52,940 Love is the same word, but it doesn't carry completely the same meaning. 161 00:15:53,270 --> 00:15:58,070 Yeah. Unconditional means that you don't make any assumption on the eavesdropper. 162 00:16:00,510 --> 00:16:03,930 Unconditional love normal. You don't make any assumption on your partner. So somehow. 163 00:16:04,800 --> 00:16:10,290 So Heisenberg may be doing something wrong and he's not covered by these proofs. 164 00:16:10,860 --> 00:16:14,820 What is proof cover is that whatever the eavesdropper does in the middle. 165 00:16:14,970 --> 00:16:20,970 Assuming I listen to everything very well, we can guarantee security of the polygraph. 166 00:16:23,890 --> 00:16:28,120 The first stretch proves just what I like. History. So the first such proof 1998, my youth. 167 00:16:28,120 --> 00:16:34,480 Nobody understood it. In 2001 shot in basket this one people understood it was much more easy to follow. 168 00:16:35,290 --> 00:16:43,090 Nowadays the framework that we use is has been developed if not well knowing this P.G. theses in those years. 169 00:16:43,450 --> 00:16:46,839 And again that's a statement about unconditional security. 170 00:16:46,840 --> 00:16:52,510 Let me say it again that a quantum solution is probably secured against the most general attack 171 00:16:52,510 --> 00:16:57,639 of these Dr. is expected because the security is based on the laws of physics and whatever, 172 00:16:57,640 --> 00:17:01,870 however powerful is not very he or she cannot break the laws of physics. 173 00:17:01,870 --> 00:17:11,440 So. When I entered this field in the year 2000, quantum information was many told win thanks to the following thing. 174 00:17:11,470 --> 00:17:15,520 Essentially, you know why these have been very useful? 175 00:17:15,730 --> 00:17:19,480 Essentially because they shut up the unbelievers, right? 176 00:17:19,810 --> 00:17:27,220 So those who still hope that quantum mechanics could be formulated in terms of local variables and keep to determinism and whatever, 177 00:17:27,610 --> 00:17:31,270 you know, that's it. We've proved them wrong. Now. 178 00:17:32,630 --> 00:17:40,150 Shut up and went entanglement in theory. And so for applications, we don't need them, we need entanglements in other things. 179 00:17:40,150 --> 00:17:47,140 So essentially that was a situation of inequalities at and your 2000 2005. 180 00:17:50,370 --> 00:17:56,890 But something happened. And what happened is these. 181 00:18:00,360 --> 00:18:04,349 These guys, Antonio Seem, who's in Barcelona. Nicolas is on Geneva. 182 00:18:04,350 --> 00:18:11,309 At least my son is was in UCL and this moment. They come up with the following observation that is not that deep. 183 00:18:11,310 --> 00:18:22,920 Once you notice it, is that the ideal coalitions of these b b 92 Protocol VBA 92 can be obtained classically without any quantum. 184 00:18:23,130 --> 00:18:31,050 And here how you do it. So to this source, whatever it is, is sending two classical beats to Alice and two classical beats to both. 185 00:18:32,610 --> 00:18:38,440 Classical zeros and ones. Now suppose that these beets are built in the following way. 186 00:18:38,950 --> 00:18:45,310 One possibility is that both of these beads are plus and also both bob beads a plus. 187 00:18:46,120 --> 00:18:50,280 Another possibility is that the first bit of is plus and the second is minus. 188 00:18:50,290 --> 00:18:55,670 And the same for Bob. The other possibility is the opposite of these, and the last person needs all of us. 189 00:18:56,150 --> 00:19:00,230 So these are really classical. There is no quantum physics here, right there. Just I've just written down the list. 190 00:19:00,470 --> 00:19:03,590 The results are pre-existing. But look at the correlations. 191 00:19:08,080 --> 00:19:11,860 But if both measures, then they have the same result. 192 00:19:13,230 --> 00:19:19,170 If both Measure X, they have the same result and if they measure X instead they are completely randomised. 193 00:19:22,240 --> 00:19:25,540 So this should ring alarm bell, right? 194 00:19:25,780 --> 00:19:33,100 We have unconditional security proof that according to quantum theory, the laws of physics prevent an eavesdropper from knowing these. 195 00:19:33,430 --> 00:19:36,969 And these can be done with classical physics. 196 00:19:36,970 --> 00:19:42,220 No, quantum, nothing. So what's happening here? Are all the security proofs wrong? 197 00:19:44,650 --> 00:19:52,240 And the answer is no, they are not. They were correct, but they gave a hint before what went on, that there were some assumptions. 198 00:19:53,590 --> 00:20:00,460 So the assumptions the assumptions on the devices are very simple. So remember I told you we moved on conditional security against these doorbell. 199 00:20:02,260 --> 00:20:10,000 But we made assumptions on what that is. And probably and the assumption was that the source of producing quantum bits. 200 00:20:10,870 --> 00:20:14,800 My source now the classical one is producing two bits, two and two. 201 00:20:15,610 --> 00:20:23,870 So they mentioned four. If I stick to one beat even once, only quantum beat and there are something about the measurements, 202 00:20:24,410 --> 00:20:31,730 then they are conditional security proofs go through. Then those correlations you can only achieve with a maximally entangled state of two humans. 203 00:20:33,470 --> 00:20:41,450 So you see how an undesired assumption or unnoticed, obvious to everybody, everything is within quantum information anyway, right? 204 00:20:42,080 --> 00:20:46,639 But those of us, for me, the quantum information, we love humans. So let's work with cubits. 205 00:20:46,640 --> 00:20:52,660 Well, that was an assumption. And now maybe you see where I'm going. 206 00:20:53,410 --> 00:21:00,670 So the bell violation is device independent. The Bell violation does not need me to assume that these are fraudulent, that these are them. 207 00:21:00,680 --> 00:21:09,340 So these are cubits. So can one look back and now have a security proof of cryptography based on the violation of a inequality? 208 00:21:10,900 --> 00:21:14,650 And the answer is yes, we can. We are in American politics these days. 209 00:21:16,930 --> 00:21:24,759 So that's the paper where the word device in the pen was first used. The collaboration between people in Barcelona, Geneva and somewhere in Belgium. 210 00:21:24,760 --> 00:21:28,310 In Brussels. Uh. Well. 211 00:21:28,360 --> 00:21:32,110 Well, not too much. I understand what we have done there in the paper. 212 00:21:32,620 --> 00:21:41,500 I just want to stress that by sheer coincidence, this colloquium comes as close as it gets with the 10th anniversary of the submission of this paper. 213 00:21:42,520 --> 00:21:47,170 I didn't plan it, but I noticed after when I printed this slide. 214 00:21:48,880 --> 00:21:57,130 Okay. So let me summarise the story so far. Here it is. As you can imagine, there's much more coming up because a whole bunch of empty stuff here. 215 00:21:57,460 --> 00:22:04,510 But so essentially cryptography. We had BP 84 E 91 cap 91 using bell inequality. 216 00:22:04,510 --> 00:22:07,270 So somehow we put it at the intersection between cryptography and bell. 217 00:22:07,990 --> 00:22:14,530 There is this sort of critical comment by Ben Emberson in Melbourne saying we don't need these bell inequalities. 218 00:22:14,530 --> 00:22:18,640 It's exactly the same as the BP 84 thing. These are these sort of security proofs. 219 00:22:19,150 --> 00:22:24,970 However, I think his own my son has noticed that BBM 92 has these. 220 00:22:25,360 --> 00:22:30,580 The correlations can be obtained with purely classical means if you don't make this assumption of cubits. 221 00:22:30,820 --> 00:22:37,910 And this leads to the device independent paper. Now, let me complicate a little bit the story, because. 222 00:22:39,060 --> 00:22:45,910 It actually went like these. So I think she's on it must honest didn't get their idea. 223 00:22:46,360 --> 00:22:50,320 Waking up in the morning one day and having a stroke of genius. 224 00:22:51,460 --> 00:22:56,090 And the story is extremely convoluted. So this path. 225 00:22:57,330 --> 00:23:01,060 Is Will. And I'm going to tell you what this puff piece. 226 00:23:01,810 --> 00:23:05,700 So. If you have to bring back something on the stove, please remember. 227 00:23:06,030 --> 00:23:11,130 How the [INAUDIBLE] did they find this very simple idea coming from such a complicated path? 228 00:23:12,060 --> 00:23:16,050 So what trigger that these paper. Is this paper. 229 00:23:16,380 --> 00:23:18,330 And what we get is what is this? What's let's start here. 230 00:23:18,750 --> 00:23:23,760 And even before starting here, I have to introduce a notion because oh, there was another thing that I would mention later. 231 00:23:23,760 --> 00:23:33,420 There's something else and you'll come back later. Are you going to use the notion of no signalling that what is no signalling is these? 232 00:23:33,780 --> 00:23:37,560 It means that Anderson, Bob can be correlated, but. 233 00:23:39,250 --> 00:23:46,780 They cannot use the coalitions they share to send a message. Let me give you an example of not seeing any resource share the randomness. 234 00:23:49,340 --> 00:23:56,720 If by quantum key distribution or by just giving my piece of paper to Vlatko, we share a common list of things. 235 00:23:57,380 --> 00:24:04,460 And then I go to I go back to Singapore. Vlatko stays here by by doing anything on my piece of paper. 236 00:24:05,390 --> 00:24:09,220 Nothing will happen on Vlatko side. I can change the digits. 237 00:24:09,230 --> 00:24:15,050 I can burn the paper. I can lose it in the play. Whatever happens, Black doesn't notice anything. 238 00:24:15,770 --> 00:24:19,540 This means it's a resource. We share some correlations, but is no signalling. 239 00:24:20,830 --> 00:24:24,120 He doesn't. What did I do on my side? It doesn't send a message to him. 240 00:24:24,130 --> 00:24:28,340 I need to send something to him in order to. To saying something. 241 00:24:28,390 --> 00:24:36,410 Yeah. Now, as you certainly know, it is a pretty good example of why we do have this pretty good example because as you certainly know, 242 00:24:36,410 --> 00:24:38,690 quantum entanglement is also of this type. 243 00:24:39,920 --> 00:24:47,330 If I share entanglement with someone, if I make measurements on this particle, the statistics on the other side don't change. 244 00:24:49,020 --> 00:24:55,860 I cannot send a message by just measuring on my side a half of an entangled pair and hoping 245 00:24:55,860 --> 00:25:01,320 that the guy that keeps the other half sees anything changing on his side or her side. 246 00:25:02,420 --> 00:25:06,590 Okay. So sharing an entangled pair is another signalling resource. 247 00:25:10,090 --> 00:25:18,580 And. By the way, I should mention that if I can send a signal the evolution of why these trivial. 248 00:25:22,070 --> 00:25:27,230 If you don't know what he's up to, maybe not obvious, but if I send a signal, any coalition can be established. 249 00:25:27,470 --> 00:25:33,170 I can tell you a little. If someone asked you this question, reply that way if someone asks you the other question is by the other way, 250 00:25:33,170 --> 00:25:36,680 so any kind of combinations can be established. If I can say nothing. 251 00:25:36,710 --> 00:25:45,140 So what is intrinsically interesting with quantum mechanics is that the bilinguals are violated by these entangled states that are not signalling. 252 00:25:45,140 --> 00:25:46,880 So there is no message going on. 253 00:25:47,420 --> 00:25:53,389 And as you know, the experiments are arranged in such a way that if there were a message that would travel faster than light, 254 00:25:53,390 --> 00:25:56,660 that's the reason why to shut up the crackpots. 255 00:25:56,990 --> 00:26:01,700 They organise the thing like that. But if you believe it to be in quantum theory, you already know that there's no signal going on. 256 00:26:03,030 --> 00:26:11,230 So why introduce this notion? Because the 1984 paper of Perpetual and Haulage is essentially these. 257 00:26:12,630 --> 00:26:14,100 He's asking the question. 258 00:26:15,770 --> 00:26:27,320 Can it be that the physical principle that defines quantum physics is the following We can violate the inequality without signalling. 259 00:26:30,280 --> 00:26:34,060 What do you mean by physical principle, defining quantum theory? Well, how do you define quantum theory? 260 00:26:36,240 --> 00:26:39,360 Hilbert spaces operators. 261 00:26:39,810 --> 00:26:44,070 Linear unitary reversing. This is doesn't sound like very physical, right? 262 00:26:45,060 --> 00:26:48,750 It works. And the first one to say don't want to modify it easily. 263 00:26:48,750 --> 00:26:54,410 Okay, but it works. But we don't know. Knowing that we have to go beyond classical theory. 264 00:26:54,420 --> 00:27:00,030 We don't know why we ended up with a Hilbert space, with a vector space, and not with a more complicated stuff. 265 00:27:00,030 --> 00:27:03,680 So I could be completely different. One. The fact it works. 266 00:27:04,010 --> 00:27:06,640 And of course, the old kind of construction, see if I can justify these. 267 00:27:07,310 --> 00:27:12,470 But so these guys ask this question is it possible that quantum theory ultimately is the most. 268 00:27:14,220 --> 00:27:21,030 Or the unique possible physical theory in which we can veritable inequality without signalling. 269 00:27:21,690 --> 00:27:28,440 And they came up with Answer No, it's not. So when there is an object, you forget about it. 270 00:27:28,450 --> 00:27:37,920 But essentially the answer was the no signalling physical principle identifies more than quantum physics is bigger. 271 00:27:41,570 --> 00:27:47,630 Or of course, as usual. Other people had the idea before, but they were duly cited, but forgotten later. 272 00:27:47,670 --> 00:27:52,160 Now this is just a. So here is what? 273 00:27:54,160 --> 00:28:00,610 Remember we had two papers the HK, but I probably can't to Barrett only if he's in the home, but otherwise he's looking the across the road. 274 00:28:01,660 --> 00:28:06,310 Jonathan Barratt And Lucien Hardy is in Perimeter Abbey on Kent is in Cambridge. 275 00:28:08,030 --> 00:28:11,110 So they ask the following. Very interesting question they asked. 276 00:28:12,240 --> 00:28:17,410 Given that. We can. 277 00:28:19,100 --> 00:28:25,819 Let's look at this. Suppose that one day quantum theory is superseded by some other more general theory. 278 00:28:25,820 --> 00:28:34,940 But this idea of no signalling escape so you still cannot communicate faster than light in any possible frame is just that with these correlations. 279 00:28:34,940 --> 00:28:40,610 But maybe more than those that are allowed by quantum physics, can we still prove security of cryptography? 280 00:28:41,330 --> 00:28:46,730 You know, at the end of the day, all the security of quantum cryptography is based on the fact that quantum theory is correct. 281 00:28:47,920 --> 00:28:52,570 The day when quantum theory is proved wrong or partially incorrect, 282 00:28:52,960 --> 00:28:56,710 we will have to revisit all the security proofs of quantum crypto this guy has asked. 283 00:28:57,700 --> 00:29:01,809 Suppose a quantum theory collapses or is replaced by something more general. 284 00:29:01,810 --> 00:29:08,680 But nothing. Nothing is kept. I always see safe in cryptography and they answer somehow yes. 285 00:29:11,860 --> 00:29:21,700 And so here you may ask. Well, but if they ask this question with the story I told you now, why I didn't throw a natural from here to ballot. 286 00:29:21,700 --> 00:29:27,690 How then can. It sounds like these are the guys who are going to rescue from oblivion. 287 00:29:27,870 --> 00:29:30,899 Not not oblivion. Strictly speaking, he was very much cited. 288 00:29:30,900 --> 00:29:40,290 But from being confused with the BBM 92 with the argument, the answer is this is for me, 289 00:29:40,290 --> 00:29:45,580 one of the mysteries of my field is a small mystery and I think nothing very big. 290 00:29:45,900 --> 00:29:49,320 But they got it completely wrong. 291 00:29:50,640 --> 00:29:54,180 And these are very smart people. But somehow the pressure of. 292 00:29:56,130 --> 00:30:06,480 The custom read what they've written. It's interesting to note is that the quantum key distribution, whatever what it performs, untestable inequality, 293 00:30:07,200 --> 00:30:11,460 it may appear as if nonlocality the violation by the inequality is played a crucial role there. 294 00:30:11,700 --> 00:30:18,120 However, if not, why or because there we use the inquiry for a different purpose. 295 00:30:18,120 --> 00:30:21,990 And as proved by VBM in 92, it doesn't matter. 296 00:30:23,700 --> 00:30:31,140 So why they got it song? I don't know. I'm very happy because it allowed me and my friends to be the ones who got it right. 297 00:30:35,020 --> 00:30:38,530 So here is a summary of device independent distribution. 298 00:30:38,830 --> 00:30:41,860 What happened after all these things? Very quickly. 299 00:30:42,130 --> 00:30:44,700 So we have Britannica in 2005. 300 00:30:44,710 --> 00:30:53,860 They have a general security proof, but zero key means you can get one bit of security after infinitely many rounds of the experiment. 301 00:30:55,120 --> 00:30:58,870 Normally you don't have too much time to wait. So essentially zero, right. 302 00:30:59,590 --> 00:31:07,569 These guys, they had a finite field, but only some attacks against these no signalling adversary. 303 00:31:07,570 --> 00:31:11,110 These advancing is more than quantum and then whatever. 304 00:31:11,650 --> 00:31:15,670 And. Well. Not finished yet. 305 00:31:17,320 --> 00:31:25,120 Now what happened? If we bring back our good quantum theory, we say, okay, forget about all these this thing we like. 306 00:31:25,120 --> 00:31:31,270 Let's believe in quantum theory for the moment. And so they thought that can only distribute resources are compatible with quantum theory. 307 00:31:31,540 --> 00:31:35,680 That's the ideal back up. Of course at the beginning that's the idea of this device, independent data. 308 00:31:36,640 --> 00:31:41,290 And now recently there have been developments that maybe these words are a bit too technical for most of you, 309 00:31:41,290 --> 00:31:49,320 but for some of those who you can read them, there are very interesting developments where essentially they proved that the and 310 00:31:49,360 --> 00:31:55,120 condition security proofs can be done and they are very similar to the result we got here. 311 00:31:57,670 --> 00:32:05,920 So it works and well about experiments and in in key distribution it's a bit difficult in for for device independent. 312 00:32:07,300 --> 00:32:10,690 Anyway, the show goes on. So we are here now. 313 00:32:12,490 --> 00:32:17,709 Let me summarise. So here we have a cup of pasta and only here in the middle I put everything. 314 00:32:17,710 --> 00:32:24,340 I put Bartunek and I think it is on my Sundays and in our paper, all this bunch of things. 315 00:32:24,910 --> 00:32:28,930 So what happens late that what happens later is that this idea of device independent took off. 316 00:32:29,940 --> 00:32:32,910 So finally, BELLINI Quality is really useful for something. 317 00:32:33,660 --> 00:32:40,680 You can test the violation or the security of your protocol, cryptography, without knowing anything of what's going on. 318 00:32:42,340 --> 00:32:43,210 It's pretty remarkable. 319 00:32:43,750 --> 00:32:50,320 You can buy two black boxes and test without knowing anything of quantum theory, without being experimenters, without opening them. 320 00:32:50,500 --> 00:32:54,970 You could test in principle that these guys give you unconditional security according to laws of physics. 321 00:32:55,750 --> 00:32:58,870 Black box security proof. That's pretty nice. 322 00:32:58,870 --> 00:33:07,180 And people started thinking. And one thing that happened is these device independent randomness generation you know handling this is how saw. 323 00:33:09,700 --> 00:33:13,959 In many cases, right? You can use it to run Monte Carlo simulations. 324 00:33:13,960 --> 00:33:19,210 You can use it to uh, uh, for cryptography to, to, to generate keys. 325 00:33:19,330 --> 00:33:26,020 You can use for many other things you can use to test software that are too complicated to test anonymized benchmarking and whatever is called. 326 00:33:27,530 --> 00:33:36,280 So what happened there? Well, people noticed that the. You can assess randomness in a device independent way. 327 00:33:36,490 --> 00:33:40,710 Now, wait a second, Mr. Billy. How, counsellor, this comes after cryptography, right? 328 00:33:40,720 --> 00:33:47,670 Because at the end of the day. Quantum key distribution means generate a random list between two people. 329 00:33:49,420 --> 00:33:54,670 Random for everyone. Yes, I. So, Alison. But nobody else knows anything about this list. 330 00:33:55,300 --> 00:33:59,290 Now, if you can generate randomness at a distance, you can simply generate randomness. 331 00:34:01,100 --> 00:34:08,600 Without the distance. Right. So it logically randomness should come before you could. 332 00:34:10,280 --> 00:34:14,170 It's the idea that the results from all three exist. 333 00:34:14,180 --> 00:34:19,850 So when I make a measurement, I generate randomness and I can use this beats to generate randomness. 334 00:34:21,740 --> 00:34:31,090 So what happened there? Okay. Let me tell you what happened is that indeed, there were before some random number generator based on quantum devices. 335 00:34:31,220 --> 00:34:34,550 This one is commercial. Year on the year 2000. 336 00:34:36,670 --> 00:34:41,640 But what happened is that in order to certify these devices, you need to open the box. 337 00:34:42,930 --> 00:34:46,950 And now at this point, you see there is no advantage of being quantum. 338 00:34:48,630 --> 00:34:54,210 Because I can generate randomness that we need in the lab just for fun to show to the students by taking a resistor. 339 00:34:54,480 --> 00:34:59,450 Most of you probably know that. Connect the resistor to a voltmeter without current. 340 00:34:59,840 --> 00:35:07,969 You say what is the voltage? Zero 12 zero. Yes, but there is thermal fluctuations and if your voltmeter is good enough, it sees fluctuations. 341 00:35:07,970 --> 00:35:14,260 You can generate random numbers by thermal fluctuation of the resistor. What's the point of that is normally you catch the radio. 342 00:35:15,160 --> 00:35:22,090 Well, it's an antenna. And so you normally so you have to get rid of the radio. So bottom line, if you have a device that you need to characterise. 343 00:35:23,480 --> 00:35:26,870 Any way to go for Quantum or to go for classical? 344 00:35:26,900 --> 00:35:33,770 It doesn't really change much. What may change is whether this guy is much faster than his sister is much more stable. 345 00:35:33,980 --> 00:35:38,299 You know, a lot of this stuff depends on the temperature by definition. 346 00:35:38,300 --> 00:35:43,010 And so maybe this guy doesn't depend too much on the temperature. So there can be some advantages. 347 00:35:43,010 --> 00:35:48,889 But I'm not very I mean, this one is cheaper, is much better, is not done, by the way, now, because this store is much cheaper. 348 00:35:48,890 --> 00:35:53,180 This guy is by €200. So. 349 00:35:54,000 --> 00:36:01,790 So before device independent, there was no real advantage in generating random numbers by quantum physics. 350 00:36:01,790 --> 00:36:04,910 There was only an advantage in generic. These are the numbers at a distance. 351 00:36:05,390 --> 00:36:09,740 That was. Yes. That that cannot be done classically. But in generating them here. 352 00:36:10,670 --> 00:36:18,800 Who cares? Now, of course, now device independent does provide the quantum advantage because now with device independent generation of randomness, 353 00:36:19,580 --> 00:36:26,390 I can generate randomness without opening the box. I can certify that my device is producing randomness. 354 00:36:27,710 --> 00:36:35,410 Without knowing what the device is actually doing. And this is pretty cute if you think about it, because it contradicts these. 355 00:36:37,110 --> 00:36:40,610 Which is the most accurate, scientifically accurate cartoon of Dilbert. 356 00:36:40,620 --> 00:36:44,580 All the others are managerial actuarial, of course, but this one. 357 00:36:45,030 --> 00:36:50,519 So this is the random number generator of the accounts department. And then producing this list? 358 00:36:50,520 --> 00:36:53,640 Not so well. I'm sure that's on them. That's what you can now be sure. 359 00:36:54,960 --> 00:37:01,630 It's perfectly correct. It's perfectly correct for what the philosopher called output randomness or. 360 00:37:04,010 --> 00:37:09,770 Part of the randomness, which means by looking at the list of what comes out, you cannot justify randomness. 361 00:37:10,430 --> 00:37:14,300 But what about process randomness to certify that the process. 362 00:37:15,550 --> 00:37:18,790 Is generating these numbers without being pre-established. 363 00:37:20,650 --> 00:37:24,370 And the process is that's what quantum mechanics can certify for you. Device independence. 364 00:37:24,370 --> 00:37:32,470 So we devised a certification. We could certify that this guy, even if it happens to be generating a list of zeros for one hour, 365 00:37:32,770 --> 00:37:38,890 it's actually really generating a random pulse, of course. I mean, there is a bit of Bayesian reasoning here, right? 366 00:37:39,370 --> 00:37:44,099 If I. And what if a generic New Zealand company that can operate in quality? 367 00:37:44,100 --> 00:37:46,770 So at some point the guy must polish some ones, but. 368 00:37:48,460 --> 00:37:55,000 You get the idea that in principle, given only the least, you can simplify the arguments of the least. 369 00:37:56,240 --> 00:38:01,670 But with this violation of any record, you can testify that the process is really generating randomness. 370 00:38:01,670 --> 00:38:06,290 Why? Because the process is not reading from pre-existing values. 371 00:38:08,740 --> 00:38:13,760 Okay. Great. So of course, yeah. I mean, I cited only one or two papers, but, you know. 372 00:38:15,170 --> 00:38:20,570 Papers and money. I got arrangements for working on the got a grant to work in tandem. 373 00:38:20,870 --> 00:38:24,949 Other people need. Fine. So here we are from consumption. 374 00:38:24,950 --> 00:38:28,670 We've got randomness. The last thing I want to mention is this. 375 00:38:29,600 --> 00:38:41,680 The other side, what is called self-testing. So you may remember I left out this work of my SNL because in fact, I will tell you why. 376 00:38:41,710 --> 00:38:49,420 If in fact, they didn't really go to key distribution, that they wanted to go here and they inspired us to go here. 377 00:38:49,450 --> 00:38:55,299 But what they proved is these and another people at one of only some of the best was in Bristol, by the way. 378 00:38:55,300 --> 00:38:58,600 So many British people, people working in here in this country. 379 00:39:00,430 --> 00:39:05,110 Daniel only he is in iceland and they came up with the idea of testing. 380 00:39:06,940 --> 00:39:14,350 And let me tell you what that is. So the best way to introduce Self-testing is by not by citing these people by slightly later, 381 00:39:14,440 --> 00:39:19,929 even by a mathematician genius called salesman who has proved essentially everything that we are. 382 00:39:19,930 --> 00:39:23,620 We have to prove to the point that nobody has noticed them for some time. 383 00:39:23,620 --> 00:39:30,160 And then and now we are discovering all these results is the greatest danger of people working in this field to believe they have a theory. 384 00:39:30,250 --> 00:39:34,900 And at some point you check people to see one of 1994, you find, oops, he had it. 385 00:39:36,610 --> 00:39:39,700 Okay. So that's the result of that. That's what citizens summarise is. 386 00:39:39,700 --> 00:39:42,850 Let me read for you. Let's don't don't read everything. 387 00:39:43,780 --> 00:39:45,940 By the way, the abstract is very cute right after these. 388 00:39:46,120 --> 00:39:51,760 This is the whole abstract for all the six new theorems without proof and 11 problems are presented easily. 389 00:39:51,820 --> 00:39:58,810 You build inequalities. Okay. And look at. 390 00:39:59,050 --> 00:40:06,740 Look what's written here in the square. Each State maximally violating the Belzer legislation of quality. 391 00:40:07,850 --> 00:40:14,749 So these inequalities I told you something like A is smaller than something and then you can violate 392 00:40:14,750 --> 00:40:19,360 by showing that is it becomes bigger than something and at some point it cannot become too big. 393 00:40:19,370 --> 00:40:28,999 So there is a boundary there. So each they devoted maximal decision is essentially the same as the singular state of a philosophy one particle. 394 00:40:29,000 --> 00:40:37,460 Finally, a language that refuses to get on the stand. Remember, spin half particle state of x equals zero of the sum of two angular momentum one half. 395 00:40:39,000 --> 00:40:42,120 For quantum information. Up. Down. Minus, down, up. 396 00:40:43,670 --> 00:40:47,300 The same state as two electrons in a molecule in the same orbital. 397 00:40:47,330 --> 00:40:51,800 When you have anti-Semitism, that's as simple as it gets. 398 00:40:53,250 --> 00:40:56,610 But the signal is strong, you see, because it's not the opposite. 399 00:40:58,480 --> 00:41:03,700 It's not. If I have the singlet state of the particle, I can maximally violate the clinic. 400 00:41:03,940 --> 00:41:08,840 That's a trivial exercise for quantum mechanics. One. It's the opposite. 401 00:41:09,680 --> 00:41:14,890 If I see that violation, it can only come. From that state's. 402 00:41:15,970 --> 00:41:19,880 I see a single number. Or some statistics. 403 00:41:20,270 --> 00:41:23,820 And I know the quantum state. And the measurements. 404 00:41:24,000 --> 00:41:27,780 He doesn't mention it, but I also know that the measurements are neutral, unbiased places. 405 00:41:31,430 --> 00:41:34,910 It's pretty nice, right? Classic. A signature of a quantum state. 406 00:41:35,270 --> 00:41:39,139 You see statistics. You know the state you're going to think of. 407 00:41:39,140 --> 00:41:43,510 What? Of two photons of two atoms or two Bose-Einstein condensate. 408 00:41:44,170 --> 00:41:47,229 There is somewhere here and somewhere there a cubit. 409 00:41:47,230 --> 00:41:51,840 And they are maximally entangled. And. 410 00:41:55,800 --> 00:42:00,210 Now you see this guy gives a serious person gives the references. 411 00:42:01,140 --> 00:42:05,850 There is a pompous quality in 92, but he finds S.W. 87. 412 00:42:07,170 --> 00:42:10,200 Page 2442. 413 00:42:10,210 --> 00:42:17,160 Now this looks suspicious. When ever have you seen someone signing a paper giving the page? 414 00:42:18,140 --> 00:42:22,330 Why does he do that? Oh, well, there was a reason. 415 00:42:22,760 --> 00:42:27,649 And the reason is that that paper is this one. If you don't have them. 416 00:42:27,650 --> 00:42:31,550 That is one of the best mathematical physicists around. At the time, he was a young fellow. 417 00:42:33,000 --> 00:42:41,700 And so these guys like Benny Liquides and Quantum 51 General setting a fight with the Alpha Sea Star Algebras, 418 00:42:43,350 --> 00:42:45,320 whatever it looks like a bit mathematical. 419 00:42:45,330 --> 00:42:51,000 And indeed, you have to go to the page that the citizens kindly point out to you to find the following theorem. 420 00:42:53,210 --> 00:42:57,200 That's the same theorem as I told you before. Okay. If is equal to square out of two, 421 00:42:57,200 --> 00:43:02,629 which means the maximum element 18 the corresponding elements whatever from realisation of power has been matrices 422 00:43:02,630 --> 00:43:09,290 never implies that something these are precisely realising that what neither the description of this experiment. 423 00:43:11,080 --> 00:43:14,080 With some systems algebra notation. So that's the theorem. 424 00:43:15,010 --> 00:43:18,760 That honestly, very few people in fact, how did I get to know about this? 425 00:43:18,970 --> 00:43:26,350 Because once I was giving a talk about this topic and Vanna was in the room and he told me, you know what, I think I proved that thing before. 426 00:43:27,490 --> 00:43:31,090 And then I took some. He must be one of my papers. I stopped the browsing. 427 00:43:31,090 --> 00:43:34,450 I saw how to find. Okay. This is citation. Finally is here for you. 428 00:43:37,350 --> 00:43:44,380 So. Okay, that's the in fact, that's the first proof of that statement. Then when all is calm and clarified the thing, read their upset. 429 00:43:45,330 --> 00:43:51,340 We identify all states of two particles which are massive inequality, the straightforward extension of a single state or to spinoff. 430 00:43:51,370 --> 00:43:57,750 Okay, very clear. These I can also understand, and it's essentially the theorem that I was mentioning before. 431 00:43:57,960 --> 00:44:01,980 Now, this series of papers has no connection whatsoever with applications. 432 00:44:03,480 --> 00:44:09,540 This is a paper about inequalities, foundations. We have this, but inequality, if it's maximally violated. 433 00:44:10,650 --> 00:44:16,800 It's only state. Now the other side, there was the scalp, April 1998. 434 00:44:17,670 --> 00:44:23,460 Here it is, published in Foundations of Computer Science Proceedings of the Conference. 435 00:44:24,600 --> 00:44:34,259 And here is what they do. Title Quantum Cryptography, Imperfect Apparatus provided a part of whatever he's missing, but he's perfect. 436 00:44:34,260 --> 00:44:40,180 The proof of these people is to remove the last assumption. And they have these search checking stories by now. 437 00:44:40,180 --> 00:44:43,480 You probably guessed what they're trying to do. Um. 438 00:44:44,520 --> 00:44:51,030 Now what happens in this paper is that. They they come from cryptography. 439 00:44:53,360 --> 00:45:03,680 They don't mention Bell at all. They just take the 84 protocol or amend it, and they add something to add to save the day, 440 00:45:04,250 --> 00:45:09,319 to remove this fact that the coalitions can be obtained in a local way. But again, they they they didn't mention it like that. 441 00:45:09,320 --> 00:45:13,490 It's extremely complicated. People are going to read. They wanted to do device independent UK. 442 00:45:13,670 --> 00:45:18,920 What they ended up proving is self-testing is exactly the same as my perpetual information. 443 00:45:18,920 --> 00:45:24,590 The other is namely that their criterion certifies uniquely the singlet state. 444 00:45:26,660 --> 00:45:29,000 So incidentally, there is something also very interesting here. 445 00:45:29,240 --> 00:45:33,610 For those who are computer scientist, you may ask if they are dealing only with the ideal case. 446 00:45:33,620 --> 00:45:37,769 Why do we speak of imperfect apparatus? An experiment I would have said imperfect. 447 00:45:37,770 --> 00:45:44,149 The bathroom is not ideal either. They have noise and so on. If a computer scientist means something else, it means these. 448 00:45:44,150 --> 00:45:48,110 It means that one that works perfectly. But you don't know how. 449 00:45:50,470 --> 00:45:53,770 So it works perfectly for the task is just you don't control it. 450 00:45:53,950 --> 00:46:00,400 That's what they meant by imperfect operators. It's definitely not what an experiment would call an imperfect apparatus, 451 00:46:01,150 --> 00:46:07,120 because I think any parent would be more than happy to have something that doesn't know exactly how it works, but it works perfectly right. 452 00:46:10,560 --> 00:46:15,090 So anyway, here we are. These are device independent self testing at a glance. 453 00:46:15,150 --> 00:46:17,549 We have myosin yo one criterion, 454 00:46:17,550 --> 00:46:25,920 one signature for the quantum states CHC another signature of the two classical fingerprint things of the single state and complementary measurements. 455 00:46:27,160 --> 00:46:31,420 And just to tell you what the state of the art is of the many kind of works in this field. 456 00:46:31,750 --> 00:46:39,070 So, first of all, now we have these classical fingerprints of every pure bipartite song written in Tango State. 457 00:46:39,400 --> 00:46:42,830 So meaning. You give me any state of properties? 458 00:46:44,030 --> 00:46:50,600 And I can write down for you a classic statistics that if you go to the lab and you see that classical statistics, 459 00:46:51,290 --> 00:46:57,440 you know that state inside any pure state, your choice and many multiple state. 460 00:46:57,450 --> 00:47:04,440 So if you have three party, four partisans on the multiple, they think that democracy with robustness bounds. 461 00:47:04,460 --> 00:47:11,150 So, of course, you know, an experiment. They may say a sorry, the maximal violation of values quite really cannot make. 462 00:47:11,150 --> 00:47:16,890 I can make the maximal violation minus epsilon. Does your criterion collapse? 463 00:47:17,100 --> 00:47:24,870 And the answer is no, it doesn't. If it's minus absolute, I can tell you how far your state is from the ideal case. 464 00:47:25,740 --> 00:47:32,340 So everything is fine there. We have the robustness and the computer scientists love this thing a lot because you can 465 00:47:32,360 --> 00:47:37,799 enchaine these proofs in a very complicated way to prove ultimately blind quantum computing. 466 00:47:37,800 --> 00:47:41,760 So you could think of my box and say, this is a quantum computer. 467 00:47:43,690 --> 00:47:47,800 $200 billion. Are you willing to pay for it? Well, let's check it first. 468 00:47:48,640 --> 00:47:52,240 How do you check it? Well, you can check it. Look, it's not very practical, isn't it? 469 00:47:52,540 --> 00:47:57,880 But ideally, you check in a blind way without trusting what the manufacturer has put into the computer. 470 00:47:57,950 --> 00:48:04,150 Just sending things to check. Violation of inequalities. And if it does, at the point you say, okay, you can buy my quantum computer. 471 00:48:04,300 --> 00:48:08,950 And these these proofs must rely on this idea of some testing. 472 00:48:08,950 --> 00:48:13,420 Essentially, you say, yeah, I test that the claim is correct by checking the states. 473 00:48:15,090 --> 00:48:21,930 So I'm finishing. Let me give you just the last glance to this nice field of device independent. 474 00:48:22,140 --> 00:48:25,950 There's much more. In fact, there's something that two dimensional witness entanglement certification. 475 00:48:27,090 --> 00:48:32,910 There is what is called semi device independent, namely, you know, once you start with all the assumptions and remove all the assumptions, 476 00:48:33,270 --> 00:48:37,620 then someone comes in, say, can you put back a few of the assumptions? Like, you know. 477 00:48:37,620 --> 00:48:40,860 Yeah, I maybe I trust a little bit. 478 00:48:41,730 --> 00:48:46,650 Maybe I passed my measurements, but not my state. Maybe I passed that. 479 00:48:46,650 --> 00:48:50,160 This is a photon polarisation, so it's a cube, but I don't know my measurements. 480 00:48:50,550 --> 00:48:58,470 So we can put back some of the building blocks and create certifications that intermediate right between the the standard quantum 481 00:48:58,470 --> 00:49:03,720 one way I believe I know everything and the device in the final I believe I don't I think I can put something in between anyway. 482 00:49:03,720 --> 00:49:10,750 So that goes the story. You needed the field of bell nonlocality or violation of local realism. 483 00:49:10,750 --> 00:49:19,479 You needed the idea of cryptography. You need to combine them and then you need to do it because if you did it when it went out of here. 484 00:49:19,480 --> 00:49:27,190 So this intersection was very small for many years and it was actually an easy, crazy way by passing through these no signalling adversaries. 485 00:49:27,190 --> 00:49:36,079 And where they're one day quantum mechanics will collapse the. We've been following the randomness and this beautiful notion of self testing. 486 00:49:36,080 --> 00:49:42,460 So just keep in mind that this idea to be a quantum state, complicated as they are, they have a classical signature. 487 00:49:42,470 --> 00:49:49,830 At least they entangle pure ones. And okay, here's the summary that I essentially just did. 488 00:49:50,700 --> 00:49:54,809 I just finished with a photo of my group. Very friendly and competent people. 489 00:49:54,810 --> 00:49:59,820 And I may have a couple of positions available if someone is interested. And with these, I thank you for your attention.