 Okay Hello Good afternoon everyone while I'm waiting to To transfer my presentation to iCloud. I can just briefly talk a little bit is a great pleasure to be here in ICTP ICTP in Italy was my second home Usually I came here more frequently and I know many of you guys from 2008 back in 2008 so And I see to be essentially helped me a lot to to grow up and understanding and knowing many many great scientists in our field Including Michael Berry for example just to name a few of them Michael Berry mouse pageant and other colleagues as well, so So I know I do understand how these might be important to you guys to find connections and Possibly doing some joint work with other colleagues yeah, so As they mentioned I'm coming from a University of Ottawa in Canada. I Cloud does not work, so I have to write on the chalk Okay I'm coming from University of Ottawa in Canada and I Would say I'm a quantum guy because you observe me. I mean Superposition of being in five different Institute essentially one is the main one is you, Ottawa Max Planck Institute in Erlangen in Germany and Also a joint Center for extreme photonics in National Research Council of Canada and also Center for photonics In Canada in Ottawa and also Institute for Advanced Study in Basic Sciences in Zanjan in Iran, so and the topic of today is about a cyber security and It would be a follow-up of the lecture by Stefano and I apologize if you find some of those Talks, I mean those part of my talks to be trivial. Okay, but I don't know your background So I will go with that. I will promise you that tomorrow. I will talk about quantum internet and quantum network So tomorrow will be very Advanced I would say research activity that people around the world they are doing including my group But today I will give a brief introduction and you know The tools that you needed to perform some experiment in the laboratory so Today we were discussing why We are doing Cyber security and why we are using photons Cyber security is the one of the main concern among three others for the for humanity and Because we care a lot about security One of the example that I say I say that I don't have a cell phone Why because I believe that is not secure Until the time that you will get this quantum communication. I will not use a cell phone Okay, so why we use photons and why we are not using electrons if you go to past all of the Connection they were with via we are cables and people they were communication communicating via landline which they were essentially connected via cables to each other and Nowadays we don't use that we use photons any idea any thought no thought is so too young Is a high transmittance? Okay. Can you tell me a little bit more about that? I mean just translating a different language is losses exactly a loss is a part of that because It's easy for election to interact with other Materials an environment for photons now photons does not interact easily with other objects Of course, we have refractive index. We cannot deny that but it's much better than electrons So in the past when you had a landline Essentially, it was so easy to overstope the information What was the over stropping? Just plug a cable there and you have your own phone and connecting you can listen to other people talk What was the consequence of having such a system? I don't know if you are old enough or not like me that you may have two phones at home And you understand someone else is picking up the phone and listening to your conversation What was the effect of that person? what No privacy No, I mean when I'm picking up the phone The other person or the other two people they are talking they realize something. What's that? noise Excellent excellent. So that's the things that quantum will prevent Okay We are using these noise in the system to detect if someone is ever stropping you So don't forget the noise is really the sign of being hacked Okay, and we have no clue where the noise is coming. So we are using photons Why because does not interact too much with environment? It has interaction of course, but not too much as like electron and moreover. We are looking for noises So we start with these we are using light, right? When we are using light is a quantum object and we should understand how many different degrees of freedom light has Without these you cannot do anything with it You should understand what basis you are going to use light has Several different degrees of freedom one of them that we know very well is polarization degrees of freedom, right? Is related to vectorial nature of the light how the electric field is oscillating upon time and space? Right, how many different vectors can you get? independent for polarization To very well either HV Anti diagonal diagonal or left and right One of those fantastic So ease spin and ice I I write it as a pie and it only can take two values What about others is frequency of wavelength of light? Right, it can go to xcv or x ray or you can go to to very very long wavelength. It's really depends on you So there you can also assign a certain state to it. What's the dimensionality of these? infinity and is continuous of Course we what we have also we have phase of light and Since our telescopes our lenses all of them. They are circular We will love to decompose it in the circular basis I mean circular polar coordinate basis and the natural basis for them is like a Gaussian modes or If I want to be you want to be practical like me is a Schmidt mode, and sorry wolf mode Is is a truncation of that? So for there what you have you have a phase phase front that is quantized because the electric field is not changing and As you see the wave front is looked like a helix and is known to carrying orbitang momentum I have seen several posters that people are talking about orbitang momentum and Also, there is another Degrees of freedom which the people they have forgotten until 2012 when my Ex-supervisor and I we visited and we call it radial index or forgotten quantum number of the light and also this is a good quantum number these two the last two they are also unbounded and You can use them to to encode information So for example frequency, how can you adjust the frequency? How can you control frequency? You can have different lasers in laboratory. Do I have a laser pointer here? Yes, I should I should have So these are laser pointer Do you see it's green right and this green laser pointer is coming from second harmonic generation If there's a crystal inside of that which we need when you go with roughly speaking about 10 a 1 micron wavelength You go inside of that The energy is so high two photons that they will be absorbed and one photon will be emitted and you will get these green energy Okay, so either with linear or non-linear process you can create different wavelength Or you can have a different excitations of atoms and And moreover with the time shaping shaping the frequency you can build up specific time encoding if you Pick up certain frequency with a different coefficient if you can sum them up you may have Photons to be in superposition of time t1 and t2 and etc so time of frequency since they are conjugate quantities of each other you can write always as a as a As a Fourier transform and you will find a relation between them. So frequency is one way or time the other one So if I want to write that then that's a frequency. I supposed to write some calculation, but I cannot do that right now and polarization of the light as we discuss it can carry two quantities and in the single photon regime also This is associated to spin angular momentum of light How the light in a single photon can regime can can spin particles? How can we create spin angular momentum? Frequency we discuss how can we create spin angular momentum by the fringe of material because I'm not sure that you you have a Experimental background that's a reason I am discussing that so you can take a quarter-way plate. You have a linear polarization You pass it through the quarter-way plate. You can create left-handed You can go with other Polization, let's say 45 degrees or minus 45 degrees you will get that or you can rotate that quarter-way plate by another 45 by 90 degrees Then you will get other than a spin angular momentum quantity This can be done electronically by the way. You can do it with focal cells. You can go even to gigahertz repetition rate You can you can do these sort of things very very quickly how how can we assign and Rotate polarization states we can do it with way plates, right? How many people they are familiar with Poincare's fair All of you with blocks fair Okay, so most of the people they are coming from the solid state language. So blocks fair is very similar to Poincare to Sorry Poincare's fair is very similar to blocks fair But what we what we use it we use it for light because the spin angular momentum of light is Again to quantity it takes plus one and minus one zero is excluded due to the transfer the transfer solitude of the light There if you have a quarter-way plate with a quarter-way plate what you can do You can go the action of the pole to pole so if I have a quarter-way plate in the laboratory if I Apply a quarter-way plate the action will be changing the polarization of light from north pole to the south pole So that will be the trajectory that you will expect if you That's a that's a sorry. That's a halfway plate. The action will be going from Yes from north pole to the to the south pole and if you rotate the halfway plate what is happening the trajectory will change if You take a way plate and by rotation and adjusting the optical retardation you can essentially go to anywhere on the Poincare's fair So this is extremely useful because when you want to do polarization tomography You need to have a better knowledge of These Poincare's fair and how you map that to the measurement that you perform in the laboratory so that will be a discussion of That will be one of the subject of discussion for tomorrow I will leave it to you if you have questions you can ask me and we can we can discuss about that So blocks. Yeah blocks fair is for spinning of electron Okay, is a dimensionality is one minus one half and one half. Do you say they spin up and spin down? Then any any equal superposition will be on the equator. That's traditionally for electron blocks fair Mathematical if you want is just mapping is the isomorphism of SO3 and SU2 Okay, it's just a pictorial representation that you can have it for light because I mean since the spin of zero is Excluded we have this permission. Okay, so now Let's go to the other degrees of freedom Remember we only talk about frequency and polarization now We are talking about orbitang momentum if you talk about orbitang momentum any term Any term that you have exponential of i l phi any field that you have exponential of i l phi those beams They carry orbitang momentum for you and if you look at a single photon regime. What is happening? It carries angular momentum of plus minus H bar to H bar to H bar and and etc. So essentially is Unbounded so the space that you have it is unbounded good fantastic and Recall e power of i l phi you have it here. So and the phi is Polar angle Okay, so it means that by a full rotation. You should come back to the same physics So essentially that dictates that L should be an integer quantity not any L will go there L must be integer good and Since that terms goes to phase with a propagation that will give you planner well So if L is equal to zero the wave front will be planner if L is not zero then it twist the wave front of the light and This is what we expect and we say that those beams. They are helical beams So they are look like DNA that they are twisted and these From one phase front to the other one is a 2 pi or one wavelength So what we are talking if we are talking about one wavelength between each of those two planes. Okay. Good And if I want to look at the intensity of these beams the intensity for these beams They will be look like donut shape because the The phase at the center is undefined. This is the property of polar coordinates. I Have a good example of that So I'm coming from Canada. I'm right now. Canada is Minus five hours, right some people. They're coming from India, which is about maybe three hours plus Some people from UK minus one hour and 30 minutes. I think So we have different timing right these look like phase For different places we go to the North Pole. What is happening? What is the time there? We have no time time is singular at the North Pole. Here is exactly look like this the phase front Will take different quantities Right by Phi when we go to the to the origin the face front is singular They call these sort of beams also singular beams Okay, fantastic. I Know this quantity is infinite dimension or unbounded and About P. I don't want to talk P also is infinite dimensions. So essentially if I am allowed to talk About wave function of photon which I will talk about wave function of photon because it's not a solution to the Schrodinger equation What I have I have such superposition in The laboratory I can create a superposition Coherent or incoherent up to you of different L different P different photon number, which I didn't talk about that Different polarization and different frequency and we call these structured photons Okay, and as example what you have you have This mode which is superposition of different P different L quantity different polarization And when you sum them up you will create a photon Which is having such a special distribution for intensity which is shown with avocado color and Polarization of the single photon point by point in changing and Ellipse ellipse of polarization you will see in some region is linear some region is sick opposition and etc This is extremely extremely interesting and from the topological point of view is wonderful to simulate things in the laboratory Just to tell you one example We were able to create not with that So we were able to create the light which will when you look at the position of the light They will form a knot exactly that knot that I have you done my tie is a tie foil not that shape and Very recently also we use that for encoding prime numbers for classical communication Good. I'm not going to talk about this. But anyway these are the digits that we were able to encode and It's very unlikely that you can factor these numbers Essentially, you cannot find the prime numbers that I got those Two digits, which they are outside those two numbers, which they are one of them 364 digits Good. So we can use light even for classical communication And we know how many different degrees of freedom light has and what are those properties? Good Now we can use them for quantum key distribution, which is one section of quantum communication I'm not expecting all field of quantum communication. I'm just talking about quantum key distribution Good. When we talk about quantum cryptography Essentially what we are using There is no definite reality prior to a measurement. This is a philosophical question But I'm among those scientists that I believe that there is no reality in the world So if you have a wave function if you have a quantum state, you have no idea about the state Before the measurement when you perform the measurement you have some probability of that So these are important factor in quantum technology second There is uncertainty principle You cannot measure conjugate quantities with with certainty Delta X Delta P They are conjugate quantities. They are connected to each other via Fourier transform. You cannot you cannot measure them simultaneously Okay, there is a limit on the measurement that you perform And the last one Which Stefan also talked about that there is no cloning theorem. You cannot copy a quantum system. I Think he proved somewhere But if you want I can prove it in a different way for you and is one line of the calculation That you cannot copy a quantum system Essentially That one this one is not independent of the rest by the way And I mean three years there and as a duty. I have to tell you a story about no cloning theorem So no cloning theorem if you go back you will find a nature paper by Zurich and Can someone help me that first? Yes So it's a nature paper Which they for the first time they talk about no cloning. I Will encourage you to go to archive and find the paper a very nice archive paper by Asher Peres The famous asher press that he passed away in 2005 So he explains that how the no cloning theorem was born Essentially, they send the paper to one of those international june of theoretical physics. I think something like that and Asher Peres and Giraldi, which is he who he was some fantastic Teotician in Trieste They were reviewer of that manuscript both of them and Both of them they find the paper to be wrong But they could not find out what is wrong with the paper Specifically speaking asher press couldn't find out Giraldi in one line he draw that if This is true Then you have no you have you can speed you can communicate faster than speed of light And he in one line he wrote a no cloning theorem proof for no cloning term as a reviewer Asher press communicated with the editor and say that I don't know what's wrong with the paper But he's wrong But I will encourage you to publish the paper because I'm sure that there are smart people in the world that they can Figure it out and they can tell us what is wrong with this paper And that was the story okay, and Very recently I was also informed that someone else accidentally he draw he find the no cloning theorem 20 years before even juric and other people, but he's in the completely different context anyway No cloning theorem. I told you that is not an independent consequence of that other two I can tell you in easy way. I don't like to write mathematics because he's just learning So if there is a machine that they can do cloning what is happening? You can give me a wave function. I can make a two copy of that Perfect copy of that then what I can do on one of them I can measure the position and the other one I can measure momentum and I can violate uncertainty principle Right. I cannot do that. You can clone but in optimal way which is guaranteed By uncertainty principle and I will go back and I will talk about this as well, okay What I would say that is much broader than them is quantum contextuality which is Which is behind the quantum quantum technology that guarantees that the quantum technology can beat Okay, and can be useful not really if you talk about Uncertainty principle, etc. I would say is much broader and the contextuality of quantum mechanics is more important than this so those are the two important factors which Pedagogical is speaking I should tell you and Now I go to communication and I want to use this So usually when we talk about communication We have Alice and Bob and that doesn't come from the quantum mechanics by the way It comes from communication language Alice wants to communicate with Bob So for example, if my wife wants to talk to me She should use smoke signals nowadays because I don't have a cell phone She has to make a fire and talk to First nation people and send me signals and maybe I will be lucky. I will detect that So that's that's a way and the channel that you want to do communication can be different way We want to communicate with people. How do you do that? Either the two people they have a fixed landline, which is going with with fiber right most in nowadays is always fiber or You want to communicate from free space For example, if you want to communicate with the plane, you are not allowed to make a fiber going to the plane Doesn't make sense. You have to communicate with free space and The other one if you want to communicate with submarines You have to go through underwater that will be the subject of my talk tomorrow all of those two channels good When you define your channel Now you have to talk about the degrees of freedom that you want to use it. What do you want to use? I Just talk about few of them. I say you can use frequency You can use polarization polarization You can use special mode or you can use the quadrature that we talked about that is a continuous valuable It's up to you. Okay, so you have to understand what you are going to use to encode information and your message You key if I want to be precise Then that defines also Which sort of single for a free sort of source do you need? Do you need single photon source? Do you need squeeze source? Do you need current source? Do you need attenuated? Healy laser what do you need that defines based on what you want to go and use it? For example, if I want to go with a continuous variable, I am not allowed to use Spdc spontaneous parametric and conversion which I will talk about this as well and moreover These different degrees of freedom will define you what you should use to switch the state and basis Because you have to encode the key Then you have to have a different schemes to encode the information and flipping their states or Generating them in a different way. So I call them phase modulator. For example, you can need a phase modulator I say q plate which is one of those Knowledge that we can use it or special light modulator Interferometer or metasurfaces or whatever is up to you. Okay? Then you should choose which protocol you are going to use You have a channel you may go with protocol of BB84 Okay, or Eckert if you are using entangled photons or you can use six states Automographic protocol or you can use for example round robin child 15 or whatever in the kind in a discreet Variables that I was mentioning. Okay, and of course the protocol will define based on the space that you are going to use If you are using two-dimensional space or you are using more than two-dimensional space Then on the other side what you need you need to detect photon. So what you need you need detection system Which is sorter either you are sorting them or you are using polarization to make some sort of position measurement Okay, or you are using monochromator if I want to call it or Intensity-flat or what whatever? and that always follows by a Detection electronics because those are all Light photons, but at the end I have my own electronics that have to communicate the electronics will say to these What is what is the what is the state that they have to generate and they you should send the message and the other side also that will be detected by Detectors, which they are they can be single photon detector or our lunch for tonight detector Superconducting nanoware detectors or or silicon detectors really depends on the protocol that you are using in different degrees of freedom On the top of this This is Eve someone that wants to get information Eve has access to everything Everything including your laboratory can hack with the pulse can send a signal can send a strong Laser pulse to your system to blind you to blind your detector So Eve has access to everything in the quantum cryptography language Okay, and your Way is finding if someone is there or not Good, so let's talk about a little bit about the source. We are going step by step That's the reason that I say I'm sorry. It may be a little bit slow But you have to we have to learn all of these stuff together. I'm not sure that you know that so source good the first source that we love is Single photon source single photon is not essential is single photon. Sometimes you get more than one is spontaneous parametric down conversion How many people how many of audience they are familiar with spontaneous parametric down conversion? Okay, good, so I did a good choice to choose this How many how many of you are familiar with With a second harmonic generation anyone doesn't know second harmonic Okay, so second harmonic is this process that I explained to you There is a laser of one micrometer wavelength inside of these But I cannot see one micrometer wavelength because my eyes is not sensitive to that and more over my eyes Is made of water? So it means that one micron when it passes through the tissues will be absorbed by water there Okay, and I think that the scheme affect for One micron should be about hundred micrometer So after hundred white a hundred micrometer you have one divided by e of intensity So these one reason that I cannot see that I don't have a good detector for that. Maybe cats or dogs. They can see that What we have to do is cheap you can create them easily But you have a crystal inside of that when these high power laser is going inside of this crystal two photons will be absorbed and Then as a consequence you will get one photon But since there is a conservation of energy that photon should have a frequency which is twice of the frequency of Fundamental wavelength, okay fundamental beam. That's the reason that you will see it as a green higher energy Okay, here is completely opposite way and This one is not linear. This is non-linear in a different way. I Will tell you So you need crystals specific crystal for that that it should be cut in a specific way If you give it give give me your wavelength. I can design it for you You go usually with a high power you will laser inside of these what is happening one photon is absorbed by this crystal and Two photon will be emitted So definitely the energy of these two photons will be lower it will be lower than these But the sum of these two should be equal to the sum of these energy So the frequency some of these two frequency will give you that Good. So if that is 400 nanometer that should be if it's a symmetric way. It should be 800 nanometer All right Then this is not the only conservation rule that you have to follow the other conservation rules is conservation of Linear momentum The first photon has a linear momentum along this direction. There are the two photons They can have different linear momentum, but the sum of these two they should give you exactly the same linear momentum there So what do you call it phase matching? Okay, and If I run I want to write it in the quantum mechanical language This is the phase matching you have one photon absorbed by the crystal property, which is hidden inside inside of that Excuse me, which is given by sinc function. Then you are creating two photons You have two and a creation operator inside of that one annihilation operator inside of this you are creating two Photons of that traditionally we call them idler and signal which they have different k vectors one of them is ki The other one is ks ki and ks good You can go with degenerate case or non degenerate case Which the two photons they have identical wavelength, or they don't have identical wavelength Fantastic, so we can have different type of these crystals One type of the crystal which I'm sure that you heard about entanglement in laboratory We are creating in this way, so we call it type one. We have type zero as well I don't want to talk about type zero you go with the UV light you shine it and you will get a cone But any photon here is correlated to the other photon from the other side And if I want to decompose it in the Schmidt way is any photon in orbit on momentum degrees of freedom They are correlated to the opposite sign It's type two as well, which you will get two cons One photon here the other photon there they have identical wavelength, but they have a different linear momentum Only at the intersection of the two you will get entangled photons in polarization degrees of freedom so those are the two Experimental results, which they are not new that goes back almost to maybe 10 years ago that they have taken in a laboratory and Those were taken by a very sensitive and extremely expensive CCD camera I CCD camera the camera should be cooled down to minus 70 degrees and then you can see single photon in the laboratory and We do these sort of things for quantum imaging and ghost imaging stuff So any photon here is correlated to that one So the photon essentially the photon wave function is everywhere, but when your detector is clicking You will find it at given time at that place and the Identical time you will see the correlated one in the other for the other side They're correlated in position and Anticorrelated in momentum and we are looking at the momentum space here also the same way and Just to tell you right now we have key source that even you don't need CCD camera to see them You can see it by eyes So it's so powerful that you can see the bright spdc at the front of you Okay, and those are The crystals Is a crystal of one centimeter, which is made in a specific way is made of layer of hundred micron even below hundred micron It's periodically pulled that non-linear effect and then exponentially the game will rain rays Okay, and then you can even see it with bare eyes You can create entangled photons with their eyes and those are the images that they have recorded on a piece of glass Good So I know how to create entangled photons and also spdc in laboratory cool The other way that we talk about that we say attenuated heenie laser or attenuated laser You don't need always entangled photon to perform QKD or cryptography Sometimes you can do it even with heenie laser. You can attenuate it if you look at the distribution of Outcome of a laser that laser which you can buy it with 10 bucks You have a certain probability which is personally a distribution and you have a mean value or average number for photons That will tell you how powerful is your laser? You can attenuate it in a certain way and you can bring the average value To be around one then you suppress the rest sometimes you have More than one photon, but the probability is extremely extremely low But you have to handle it in a right way that someone cannot do photon spacing attack to your system Good any question tired Okay Good now is the time for detectors. I'm sorry is look like building a building Right, you need to know the tools without those tools. We cannot talk Now is the detector time Detectors usually what we have they are extremely by the way expensive They are more than depending on the type of detectors. They can be more than ten thousand twenty thousand They can go even to seven hundred thousand Depends on what you want to do with those detectors. I will tell you a little bit of details So these are from a company and I have a permission from them because I bought from equipment from them What do you have a photon goes inside and by the way, this is not these not a process only for Visible light it also works for x-ray. It works also for a different wavelength So light goes inside what you have you create holes Hole and electric pair of or hole and electron and then you accelerate them You change the bias and you can detect them and during this process Also, you have a cascade process or other lunch process and then you create more electrons and then you can detect it precisely okay, but those detectors They have a certain quantum efficiency What I mean by quantum efficiency any idea not exactly number of Number of photons that I can detect it after shining certain number all over them For example, if I shine hundred photons on those detectors For these case for tall spad what we call it, which is the black one. I can detect 80 of them If they are at we see at 710 nanometer. That's the reason that Most of my experiment has been done Most of those experiments have been done in in T 55 nanometer T 55 nanometer Double because it should go down conversion. It should be 710 nanometer So the spdc is 710 then you have to optimize it for that way and Most of those detectors they will not work at the telecom wavelength at the telecom wavelength They have a quantum efficiency of less than 10% so it means that out of 100 photons only 10 of them They will be detected is not the only problem of those detectors There's another big problem there Is that time? When you have the avalanche Electron is cascaded and created then it will be detected by electronics you read out by electronics that takes time Until the time that again detector is is loaded for the next pulse and we call these a Dead time for detector, which is 77 nanosecond the pulse that you create is 20 nanosecond So totally you have roughly speaking about 100 nanosecond for just detecting a single photon That dictates how many rates can you get? How many rates can I get? 10 megahertz. I Cannot get more than 10 megahertz. That's exactly what Stefano told us today that For discrete quantities you have a problem of read out. You cannot go to high rates And continuous variable is a solution Okay good Any questions so far? Yes Like this is exactly what I told you those detectors. They are about 400 to 700,000. Oh, no, no, I don't I don't know is a technology is a technology only they are folk I think so I based on when I say based on my knowledge It means that I don't have a knowledge about that But I feel that there are only four companies in the world that they are producing I have no idea about China But in Europe and in the United States, they are only for companies that are producing this with high quantum efficiency. I Have and I'm getting more of them They go to Pico second Yes, they can go to Pico second read out. Okay 10 soft because It was really really high in this way Good Any question? No, good Okay, now it is a fun part is a little bit boring, but is state generation and Detection we talk about how to generate how you can have a source All right, we talk about how to detect them to take the photons, but we did not talk about the state generation How can we stay generate the states? Yes, you you are very precise and you're very cart depends on the degrees of freedom that you do you can go with a phase modulation for example Okay, but I would prefer to go with polarization. Is that fine because he's easy Everyone knows about polarization. Let's go with polarization. How can I generate state and Detect them in the same time. We are talking about that How many of you are familiar with polarizing beams Peter? All right, is there anyone that is not familiar with polarizing beams Peter? No one so easy you are you familiar polarizing means Peter? No, you're not okay. I will tell you polarizing beams Peter is an optical device which is based on the different layers is Is look like two prisms which they are attached together between them. There are different layers What does this different layer? They have dependency of the polarization So if you go with certain polarization state what is happening? It will be reflected if you go with other different polarization It will be transmitted and you make different layers of that in such a way that you will get more of them to be Reflected and more of them to be trans and the rest will be transmitted. Okay, so and you can have different type I what I talk is what they call it dielectric one You can have a different version of these which depends on the way that you perform the experiment some of them They can get also very expensive depends on the Approach so what is happening? Usually in polarizing beams Peter if you send polarization of H? H I'm sending so the vector is oscillating this way When I get I send it it passes through these polarizing beams Peter because polarizing means Peter will allow H to be transmitted And we will be reflected good I Can detect H now so if detector down will click I know that I'm detecting polarization of H Photons with polarization of H. What about V? We will go up Brilliant so detector up will give me V detector down will give me H Now I have a measurement for H. Let's go with the other one How can I generate? Not only H and V, but I need another degrees of freedom another set of them Which the other set was mutually unbiased basis, right? Do you remember from the previous talk you need to create? The conjugate quantity of that and the conjugate quantity is a state which is in superposition Right, so it's not true that only I need H and V But also I need the conjugate of them Which the conjugate of them will be? Fourier transform discrete Fourier transform of that then it will be one of the possibility is H plus V Divide it by square root of 2 which is for normalization and the other one will be H minus V divided by square root of 2 Which traditionally if H is like that if is V is like that This state will be like this. So we call it antidiagonal and We call the other one diagonal good So you need these two you need to manipulate polarization and in order to manipulate polarization I supposed to write on the punkers field and discuss about it, but I couldn't do that so In order to do so you need wave plate to manipulate that So one of the way played for example if you go with the state of H If you go to a halfway plate at the zero angle what it does It does not change anything Right Agreed with me if I have a halfway plate, which is that zero angle if I go with H Since he's on the optical axis it will not change anything But what is happening when I change the halfway plate to 45 degrees? The polarization will rotate by twice and it will be V polarization So now I can change the polarization of H to be V and then it will be detected by up Now I have a technique that I can switch from H to V on the generation side Which is only a halfway plate and rotating them from zero to 45 degrees I will change from H to V and on the detection side. I can also detect it from up or down good Now there is another one. I have to look out for that regime that discrete Fourier transform How can I generate them when I rotate the half a plate by? 22.5 degrees when you rotate by 22.5 degrees what you will get you will get that state But now there is a problem. What is the problem? This photon is a superposition of H and V. It means that sometimes will be detected by these sometimes will be detected by that Right it is not deterministic. I cannot define this what I have to do Exactly I can place another half a plate here with minus 40 minus 22.5 and In this way if you send H H becomes a and then a will be detected by down true and Then if I send if I rotate that from 20 minus to a plus 22 Point 5 to minus 22.5. I will create the other state, which is D and it will be detected by the other side agreed so now With polarizing beam splitter and to half a plate. I can create all of those four states and I can detect them right Fantastic this is exactly what you need for basic QKD So I summarize in this way. So in order to create what these states you need this and In order to create a Anti-diagonal diagonal, which we call it conjugate quantity of that or mutual and by spaces you need these configuration and for detection side You need these or you need that Now detection and generation also is clear for me of the state is clear No question Good, yes, we can talk about that as well tomorrow Tomorrow I can talk about these which is more complicated state, but I mean I How many people they knew these before coming to these lecture all of these about single photo and stuff Only few people. Yeah, okay, not the rest. So we do these background Like we cannot talk we cannot talk about complicated Scenarios like high-dimensional QKD and etc. Tomorrow I will talk about these today I will talk about some property of high-dimensional QKD why this is useful and etc. Okay, so then I have Alice and by the way I love them and I have Bob Ali sends message to Bob Is public channel? Let's review what is happening in the public channel They will send a message and by the way, this is not the classical way that people traditionally right now. They are doing Right now is different. It's completely different But let's look at the very very simplified version of that in a public channel, which can be fiber internet Whatever you want to call it. They can they can talk to each other They would send a message and if also is there is listening to them And the message is this Is this a message? Wow Right Anyone can read that? No, okay Then what they do in a secure a secure channel. They will share The key which is a substitution key is easy Super easy key which it goes to the time of Julie Cesar, I think in Roman Emperor that they use these substitution key That you can substitute a with e be with F and etc And then if you plug there what you will see You will see these famous Poem of Hayam which I love some for the glories of this world and some sites for the prophets paradise to come ah Take the cash and let the credit go No head the the rumble of the of a distance Trump Okay, so now the message is clear and we can read this message Now we will translate that in the in the quantum way I'm telling you this is not the right way that people right now. They are using it right now They are using RSA code, which is different technique is look like sending you An envelope which is open you place your key as your message inside You close it and you will send it to me I have envelope sending to all people but the keys with me is a completely different way that people they are doing But there's a simplified version of understanding the cyber security good Now what we can do essentially a I need these conjugate quantities Which is much only and by spaces and we realize that those are needed and we talk about that we need HV or Anti-diagonal diagonal and remember When we talk about HV or anti-diagonal diagonal, I call them one of them to be zero one of them to be one Those are the beats that I'm encoding the information there. Okay, it's just a symbol for myself It can be swapped completely. It's up to you Okay, since our By the way, why we are encoding zero and one Anyone can tell me why we work with zero and one based why we are working base to nope Nope, nope For Why why why like you're right? I mean you are all right What? You are very close. Yes. Go go there. I mean to find it out when the digits all when digits all appears Shoot no Transistors Okay, that's the reason that we work with zero and ones because our transition works in this way Okay, that's the reason either current or not Okay, that's the reason that we write it in zero one so we write it zero and one if your Technology is so good that you can work with zero zero one one one zero and one zero one work with that It's totally fine. Okay, so What I know that I have two bases now Guys, I have two bases one is base of cross One is the base of plus right Do you remember that I showed to you if you don't have a halfway plate if you go with this state Sometimes you will detect it in edge. Sometimes you will detect it in v right so these two quantities They cannot be measured simultaneously So there is an uncertainty principle. Maybe I should be very careful. I should not place h bar divided by 2 There is a bond here. Okay, it means that I cannot measure these two simultaneously What I do sometimes I will create one of those and I will send the information to the other side What I'm choosing Alice. I will choose randomly one of these two Either plus or cross and then I will choose what information should be inside of them And then I will transmit them. You will see them right now. So there's a secure channel. So what it's happening Alice is creating First of all Alice toss a coin which you need a random number generator Not pseudo true number random number generator Okay, without that No, just forget about QKD. Everything should be handled properly So randomly Alice is picking up one of those bases and then she chooses which information She's going to send for example. She picks up cross and she's encoding zero She picks up cross encoding one She picks up plus encoding one and etc. So she has a sequence of pulses or photons What are the not what are the sequence of that in principle? We call it infinite is Infinitely large is not limited if he's limited that's the proof of security is will be difficult and you have to handle it properly Okay, we are not entering to this we know this because We are in a higher dimension. We understand what's going on there But indeed Bob has no idea Bob has no idea at all What Bob knows that Alice is sending some messages What Bob does? Bob also randomly picks up one of those bases and perform the measurement. Look He's not he's not measuring these he's he's picking up randomly those bases So he picks up randomly For the first one cross plus plus cross cross cross plus and etc Right and then What is happening? Alice calls Bob and says that for the first one I use Cross Second one cross third one plus and etc. What she's announcing is the Bases that she picks up and generate the state and sending to Bob not the information at all Right and the information for Bob. They understand after this communication What do you call it sifting? Essentially sometimes they are in the same base which is This this and that and that One more yes The point is that My computer when I'm working I prepare the talk at this slide explicitly at 3 in the morning And Oh, no that noisy I will talk about that I'm careful about this so and my computer has a blue killer So there is no blue color in my computer because I have to work and I don't want to be bothered So anyway, what is happening? Forget that. I'm sorry about this assuming. This is plus Okay, so just make that Okay, so what is happening then they understand both of them they understand which of those they were correct They are not announcing. What is the key inside? What what is the what is the measurement outcome? Absolutely. They are not announcing that Right. So what we know zero zero one zero. I understand there is a mistake. I didn't intentionally okay, and That's that's what we what Bob knows, but not He will not announce it publicly Okay, he will keep it what they do they have these sequence of key with a lot of those numbers which they are in the right spaces and Essentially, they should get the right information What is happening? Essentially Alice and Bob they sacrifice some of those bases that they perform the measurement in the right way Okay, there were four of them, right? There were this one This one This one and that one right what they do They sacrifice some of them what they do they announced the outcome of that so Bob announced that the outcome of these for example Was zero that one was one or whatever so That is the scenario so essentially Bob what measures was zero with essentially Alice sends one And the other one was one So then they compare how many of them they are wrong and what they have we call them Quantum beat error rate so they have in this case, which is a short key. They have 50% of the time being in wrong Essentially, it's not 50% is 75% of the time. They are right, but 25% is wrong But what they want to sacrifice they'd sacrifice only half of the key. Okay, that's what is happening essentially good, so This is the process and of course, there are a lot of electronics on the top of that electric a lot of programming You have to work with the communication, you know, I Don't want to talk about those things So I will give you let's say 10 minutes of break and I'm sorry after that We'll come back and this part of the talk will be more exciting