Yes I think the last of the actual blackboard lectures left on campus I better I really felt that to frame some of the details of quantum crypto if I wanted to go smell I could have like 50 bar lines like you guys and you would have gotten rates to Google to find out the work that I'm only giving you january speaker. So I just out. My name is foggy thing. I live in C. And you can always send me an email wanting more aggressive probation. My research is in the area of content sensitive so I use quantum mechanics but not for any drift dagger b. For due process they had some computing purposes and any new york professor asked me to give a guest lecture gateway oil degraded. You can talk about how to crack RSA using a quantum computer. And I sincerely thought about it. I don't think I can teach you guys a quantum computing business and B how to crack RSA using short minutes. Using it like a series of lectures which I'm not going to do that. I do plan to teach a course in quantum information in the near future. What I really do today is tell you guys about some of those bizarre features in quantum mechanics and how you can use it for quantum key distribution So I will not be talking about using quantum states for computing purposes just do transmit this. Does that. So before so quantum don't sorry only going to talk about why he didn't using nine going to Gaga PowerPoint computing but I'm happy to talk more. At a later time you guys are interested in kind of guy he writes to him. Okay so before I start are there any questions are you guys aware in this field of quantum information quantum computing and I have no idea What do you guys have learned I was still that you guys did learns columns. Rsa MDP helping right okay I don't know much about those things set for the fact that RSA relies on multiply big numbers and that's it. So. Okay. All right so I will heal you guys seem very basic way a quantum bit. Is it getting any kind of system you guys want to know more. There are multiple books on quantum information. This one by ski So there are five morning mouth decorum and yes. Of course what do we do redo and I went to the noisy experiment like IBM and Google are working on quantum computers they have demonstrated they can do things with up to 50 cubits. And the last the last clear implementation are Shor's algorithm. Dues saw deliver four factors Well do prime numbers demonstrate a probabilistically because all I am computing works titled statistically as it is right times. So it demonstrated a factor 50. But that was piloting everything up. And I was ten years ago. I have not been very closely following the field but I've heard that now you can do many more numbers finder client computer assisted by some classical. So it's not pure. However in the last less than five years there have been multiple breakthroughs in the area and there has been a lot of money Both by the government and by big companies like Google Microsoft IBM et cetera. And so the view this right and so while the basics of this over there I'm going to go through which is there then it can be preserved. Yes I thought deviating. Everything I forgot something is PDE4 might mean that prevented FSR. Here's what it off or. 20th t-distribution parties. The most widely used one. And in 2072 when can I demonstrate that they can use it so the problem with this is it works. It works beautifully. It's secure because of the law other mechanics that guy back there. So if they fundamentally see here however it was very difficult to transmit information because quantum states of a vital and I'll talk about that. So making them ******** meters just like that big. And that's not the point. But in 2017 Do moves one Canadian. They showed that making use VGA or widgets but I'm going to go through to translate like dew point of the distribution from a grounded and bureaucrat. And then the Chinese group and forgetting that needs that is they showed that they didn't D with B tree like satellites. And that's when now basically right oh no that's 400 millions of dollars because he started out. So so it all started with I think well the theory I do a fair amount of stuff was done in Austria and the early experiments and then it builds from there. And so expect great new results over the next few years because now that can be placed by the crypto stuff I'm going to talk about is in use right now. Probably somewhere in the Pentagon I don't know about it but definitely by banks. So break these banks this distribution systems and say oh yeah they're like several companies who sell these kids. So so this exists it is all based on light that you and I forgot to bring these polarizers. And the point is that. So do you guys know about polarization of light right so type has to polarization. It can be vertical or horizontal and a polarizer would select what flavor. So maybe like this one see me. Basically the vertical polarization is going. And so this one isn't as absorption but you can still see me because the vertical polarize it they're both like a lie. So light is going to go through it more like two. However If this is like that you don't see are like parks at the lightest either vertically or horizontally. So if this one selected only the vertical polarization to go to and I outlined this one so that only horizontal polarization went to that means all other vertical polarization to nine row two which means no life went through. So you can think of these as your basic IQ you forget the Q bar for a set it as your logic 01. So if my polarizer it my light is polarized. This way it's logic site I chose find its logic. Why it's polarized this way then it's larger than 0. It can only be one unknown when you measure you use a polarizer yet but there's a dark side like this. So so basically like if it is like this 0% of the bike with you. Let me just say that if you have a history here. Okay so I have some polarizer which is many heart. Whenever vertical I go through I'm gonna call it a. And then I have another polarizer B as some other whatever polarization angle. So we only do Let's go this way at some angle between a and b. So you know that if a and B are aligned. So neither two polarizers. If a and B are advised so theta a theta minus theta B is 0. Then all the light should symbol. Let say a 100% all night. And if it is 90 degrees Oh no like when two parties. So higher percent 0 it's 90 degrees. No lied to and I'm going to break it to you. In fact cosign squared. No advantage at all I went through and stuff. So that's what happens with life. And now when it's 45 degrees with each other then half the light pretty much goes to. So this makes sense when you have lots and lots of them. But if you are trying to transmit Single photon of light so light comes in discrete. Do you guys know so just in case someone nothing like those in discrete packets of energy. Each one is. And these discrete back these are the forgotten. If your frequency is Kinsey agree whatever you have seen the energy is some constant known as maintenance. So because this is honorary member who goes before but it's a foreign Jews dies. So simple. So there is a very small number so each photon has very very little and write neither is nothing. But the right it if you're shy if you have a single photo you can think of it as a single bit which can be polarized this way toward this right so that's your your your logic. But I'm trying to detect a single photon Gray and I have this polarizer arrangement maybe it went through the first one was work with light So then the difference between these two is 45 degrees. What would happen in a way 50% go through have a seat. Okay so why not there is no number. It's the smallest unit. So like an ICE table in half a bow guy Mozart ever thought about. It's only got four What do people council so that means like range or wherever they might be if that force. Sometimes therefore not We'll go through sometimes. And the laws of quantum mechanics dictate that basically it is an absolute decision by that guy and it's super last-minute. Oh okay I'm gonna go to this cell hemodynamic decides I don't know until you make the measurement and wanting to make them feel like Nobel guy or whatever. So that's what is variance How about client measure like a classical measurement where you could see okay. 80% I imagine many of you disagree because it's absolutely right. So so there's dissolve polar night underestimate. So this is all classical light. And then you have a signal then and now. Maybe these are aligned the forgotten will go with a 5% probability it neither and iodine whenever that four does not go through this kind of awareness I'm wasting my time writing really does not go to 40 degree a random decision. So it's random in the sense that the phone numbers you don't know it's random because doctors don't ask me where NSA. It's not. If only you could find out where that guy was thinking. So pretty much all physicists agree. Absolutely. And lastly this issue. So that's great. And that's it What really distinguishes out of it you only have two possible arrangements. Ok. So I am just going to call the horizontal Vision Zero vertical polarization logic once. Wherever you like this if you have a quantum bit guy. So classically think of a photon This is how computing is practical wisdom. If you if you dig into that yeah maybe the freedom of Beijing he doesn't live on. Well obviously it lives in a much bigger barrels or adulthood. So you can be you can be you can be whoever you want to be in between. So basically draw very well. So polarization or vertical authorization can be diagonal 45 degrees because polarization polarization has decreased by again. So this way or this way. So 45 degrees this way 45 degrees this way. And it's so hard for example these are inherited this or this. It turns out that's not yet. There's another degree of freedom. It's like up phase information. So so it can be what is known as left and right circularly polarized So these are combinations of real and imaginary part. Right realization. I'm just gonna throw you bit by bit without them. You do mention. So it can be harder thunder We were say horizontal that's our 0. Quantum A's. Vector is just shown as lipids bracket notation or suffering then. And it's basically this. And this. So all your information your v is here. And here this is your work. They go. Well this is my one. You can be like this way. That was my 4045 degrees so you can be diagonal The norms of although these have to add up to nine so that's why there's no one over square root yet do other than that that's very important. You came down. I assume you guys know so familiar algebra again sign with time. Ok so you can be right circular or that's circular And these are things you find in nature. And those can be written in this basis as one which one I guess. You guys all know linear algebra all of the effects that are orthogonal to each other. So any of these two would make or your cubits you away Yes here so you don't have to be horizontal and vertical. It's just easier for me to demonstrate it using these. You could have easily based diagonal 45 degrees this rare at this rate. They're often 90 degree the bar or Latin right circular like. So I'm really winded up about this. Yes. And I call this plus spaces or her Crawford says. So and then the last thing you need to know is a measurement. So when you make a measurement to target client bandwidth so many possibilities you will only get with your point. Because all their clientele nesters goes out the window because you will only get your ROI. Now you can say that all I didn't just you know instead of looking this way look down on it this way that script you only get a 0 or one. So you only get like right are lesser. We will only get this or this depending on which way you're looking at slackers here. So this is your z axis. If you look along z you will get horizontal. If you look along this line this event. So if you look over x you're going to get these two people. Your four that is in this 45-degree situation along x axis or something then the measurement on seed which is straightforward. I just make it go to one of these polarizers. Then again amount with a 50% probability of Senegal to 30% probability is not going to go through and it's an absolutely effective last-minute split-second decision. So that means that if you encoded information in these cubits in these base use these as your basis for 01. By mu lambda measuring here. You're going to reach because you're just going to randomly because your wife. Does that make them more subtle thing here. That if you don't choose the right way to measure your big You're not you're just getting revenue stream. So that's the important thing here. And that's what these guys relied on do apart from Ben and grasp protocol that a quantum measurement is a very invasive procedure. It destroys destroys all your coherence information. And if you don't measure it right So that they do save would be how are you going to measure this so that's what I wanna know Alice and Bob. Okay so Alice and Bob are back. And ask me questions. Okay so I will go to this folder. Also known now as Beebe 1984 B and B chemo. This impurity here is site page. So it relied on the fact. Is it means that you will pile up international in scope. So if somebody's trying to watch and you'll know about it because your client base. So practically all the implementations are BBA or protocol useful gone. So this it doesn't have to be for dance. Any quantum system with two degrees of freedom would work. But forgot I'm sorry minus two vibrators basically free space electronics or make it very far. And I hope you do. And Google are building their humans. So they're all city for Gallery refrigerator. The refrigerator. And so that can be used to transmit information. Pre white guy Richard library secret they pretty much all have implementations of EDA or use for dance. Do you guys typically fibers by banks and defense so in free space was a very recent development twins And you may have recently was never 20th Padres view. Okay so so maybe the idea is that Alice and Bob want to generate a share random secret e and e. Once you know. Alice Bob January share as would be obvious. Once you know without me Because Alice is sending a signal to Bob IV and I know about it without being detected. So that's where this security. And you can see that this security it's not grounded. You try to do something that is computationally difficult. Security is coming from nature any quantum system fortunately history if you try to measure and no matter how you try to measure Yes so that means he tried to measure it would destroy my problem is trying to measure. We're also trying to signal because the laws of quantum mechanics don't distinguish even Bob right so anybody trying to measure this signal Alice is sending is going to destroy the process design protocol. So yeah it's the correct heat in spite of doing the measurements as it's trying search quantum information and BBA or solve the measurement problem by Alice and Bob Sherry when the mesh. So the bids on which bought me some measurement they share that information and they just discard. The low foci or solve the measurement problem by just discarding the bits that are measured. Sherry All right so there are six steps and I have had to go through mass media to other side apologized for it slowly but it was very important to be clear what to deal with. So step one marker for Alice generates To random binary strings one a. So a is A1 A2 and so on and so forth. This is a string of 0's and 1's 11110 R. So that is used to create your secret. And S is some other B. And that is yeah she decides it's a random street but I'll cross n plus. So this is Alice decided. She's going to make this space has been measured or not. So these are the two different pieces. When does she sets her E2 and polygons and the polarization I forgot So basically in F i is class then he uses the basis up and vertical and horizontal. So she uses this one. This is 0. And if this is Ross bed she uses the basis basis. And this becomes one. So before ball and this is for now what Alice And then it goes up and be more moth starts receiving the phone up. Bob has a lower. He also has to generate alright Netscape sub-object rate. Above calls it Why do N and this is basically a cross or plus. So Bob comes up with his own brand-new basis in which he is going to measure this data cube. So this get a0. So that means when you yes I forgot he picks one of these spaces apparatus that measures it. He's gonna get as your one. Remember if okay so I'll go back. So then Bob Bob measures every four. They are ours and basis So measures in our races and so Bob has its own straighten them out as they generally there is no reason to assume there Alice is random string of bases is going to be two bonds random string or places right so there is absolutely no reason to assume that there are many places to be so sometimes narrow. So if this is equal that means the 0 and ones of ours like a I would be the same as. So if they both use the same basis E I the statement B I ended they are not same. Then you get a random thing. They may not see again by the point is that there is absolutely no correlation. Between EI is the thing clear to us that far. Okay so I'm always me my my father lost year over year. And I'm going to be these. If you want to know more new words. Sunnier quantum bit plots here So Alice and Bob Don's Bob measure then they both have a and B Alice and Bob each other up and share their as our vectors. So that was how random string. And this is the basis not the secret to the ad bought shares his random string. And so he helped us with their desire to make note of all the I's Si is not the same so they had chosen a different basis. That means that needed it's just garbage is that whether Rennes makes a decision by nasa that means that's where TCP. So bear S i is not equal to Yeah it was just get rid of get rid of all those data base. And so The one bits are pure garbage b. That means now you have E prime which is smaller than a because you felt your garbage width. As b prime which is smaller than B. And these are smaller by about 1.551 a random probability using this or this. So these are approximately n over too long because their safety conditions Okay so that's good. So these are good things. So now step five Hafez. And people decided that oh you don't know maybe there are some errors in transmission. Now and I think I don't want them. Asking me Mission errors. So here I'm going to pull some stuff out. Just some places. Right so Alice sends some of the bits are o prime. So and Bob measures them and they should be the same as the brand-based because they already they made measurements of the same bases that makes you happy that things change It's not so Bob estimates based on a small fraction of the BBC got how many of them were like transmission errors and then he kind of knows that. Okay so that means that I just have to deep space out because they will be lost interest which is that means if you don't transmit all of a crime do estimate what your error. You can transmit a small fraction. So not all eat right gets transmitted by only seven of them. So Bob measures bears And now he no rhyme and meter Libre that occurred at eight. And again I said hey I'm Joseph being but you don't have to set everything to estimate what your error is. Quantum mechanically visit now step by step by step six. The number of errors that you have you can think about it as the maximum information paint. Because these errors could go from hooked on something else and got it. Or it could be a full-time each detector. And then you would see that SAT or ACT and pull down on the way movie but nobody noticed. So number of errors that you have in this crowd at all gives you information on the math involved. But not. So that means wave. So how many of this you get knowledge you just replace this by something that's even shorter than that So basically overall day even not going to get an idea of how well yeah. So so that's the last step and it's a little Geneva to believe that it is trying to measure them. And then they basically get information and putting her own forgone along box way. They will know about it or either you paint the wrong basis That case this step thereby there is a finite probability in the right basis. And then they find out that these deaths. So by choosing the stream how much the fraction of this is at there was make it secure and the big idea and read more about it and understand it. But the big idea in all of these things is they use something that is defended author. You are not relying on competition So a Diffie-Hellman or RSA you're relying on computational complexity that it's just impossible. It's not impossible. Really to crack this one. It is impossible to crack. This is not difficult it's involved. So that's the difference. And so when RSA and they may have been a principal as quantum computers become better. And this also tells you what is the problem with doing it using cubits AS every problem has he's not going to solve a small rationally groundless. But the big problem in making computers is again current measurement. Once anything makes a measurement does anatomy ie it can be random air molecule. It's going to go ask the student. So they have to be done very carefully that the environment doesn't know because it doesn't have to be a fancy detector or eavesdropper dimension. It can be anything which is why you will not be mechanically because there's just that stuff around us. And smaller things came to see me to read it for lifetime. So so that's that's why making quantum computers is very difficult and very challenging materials Mies. And also because all the rules of quantum information I'm one of the rules of classical information. I don't know why. Because it's super straightforward Oh I buy a lot of errors. I can correct for them by making multiple copies. You can make multiple copies here. Because to make a multiple clock you need to know what it is. And once you find out what it is that quantum message loss. And if you make a measurement in the wrong bases it's garbage. So so so you cannot apply all the classical error correction protocols decline appears. You will have to come up with different types of error correction or to others why this is a very difficult problem. Quite complicated. It's even more complicated by adding how when Cuba interacts with another cubic which is a very powerful thing called climate that women have the time to do it. And I thought if I talk about it you get nothing out of this lecture. But that is what these non-local correlations between key races where needs quiet. So powerful. And that is That is what is emphasized it ensures algorithm to crack the RSA encryption. So why donated computers and you're very good information design will not be secure anymore. But that day is not today. A slightly now employing a lot of time a lot better by unwanted different fields to get there. In the meantime you can use to send secure information and that is being done everyday on the market. So this is one distribution and I'm happy to answer any questions What was it worth it
cpeg472-010-20190506-101000.mp4
From Andrew Novocin May 06, 2019
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