 Continue the continuation of these lectures and include in these tutorials, okay, so. Thank you. Thank you very much. So, welcome back. And today we are following the discussion of yesterday. So, I left about 45 minutes, even a little bit longer, as usual for discussion. Okay, I just noticed two people, they have questions. So, I will ask you to hold your question until the end of the slides, and then we can have some sort of discussion, okay? So, anything related to QKD that you may have problems? So, just, I want to review what we have learned yesterday together. And because that's also essential, again, without this we cannot go further. And I'm asking a question, is there anyone that missing previous lectures here in the room? Anyone missing? Okay, fantastic. Good. So, just to remember, so, when we are talking about QKD, or we are talking about quantum cryptography, this is the scheme that you should remember. The scheme is that you have Alice, which is sending message to Bob, you have certain degrees of freedom that you have to learn how to generate them, how to detect them, okay? And you have a source that is the source that you encrypt the information on. So, it can be single photon, it can be the CV, or it can be whatever that you want, weak, attenuated, you need laser or lasers. And on the other side, what you need, you need detectors. So, to detect them. And we discuss about the possibility and the problems those detectors they may have. That's the reason that you have a problem. Is there anything funny there? People have nothing, maybe I have forgotten something. Anyway, and then you may have different protocols that you may use. And the protocols will allow you to handle errors and the threshold for security. And moreover, the channel that you have it, it can be different channels. It can be fiber, it can be free space, or it can be even underwater. And today, we are explicitly targeting this section because we did not cover different channels. Good. No question here? Okay. So, and Eve, remember, is everywhere. Eve can do whatever she wants. And the effect of Eve will be errors in the system. So, and again, to remember that why high-dimensional QKD is useful, we have this curve. So, errors that you can handle and you can get a positive secret key rate is given depending on the different dimensions. And you can see that these error bit rates will increase, the threshold will increase by going to higher dimension. So, for example, if I am in the dimension two, if I go with 11% error, then I don't have a secret key. So, it means that if I'm monitoring and I'm comparing some of those keys and understanding what's going on with the bit there, if I find out that 11% of them they are wrong, then I don't have the permission to establish a QKD system because I say that there is no, there is a possibility that someone attacks to my system. So, but still with 11%, I can go to dimension four and I can have almost close to one bit of information per shifted photon. So, then going to higher dimension will really help you to increase the secret key rate. Good. So, and handling more errors in the system. Then, we remember that also we verify this. Yes. Yes. You mean if I go with more dimension, then I can go to more error handling? Yes. There is asymptotically going to a point. So, what I'm saying to you, if you plot those curves for different dimensions, let's say the dimension 100, even 124, then you will see that asymptotically all of them, they go to a point. So, you are not allowed to go beyond certain range. It doesn't go to be 100% error. Okay. What is the limit? I don't remember really, but it should be something like about 50, below 60 differently. Okay. I have a curve. You can plot these. So, just to verify this experimentally, also we built up the first high dimensional, optimal quantum cloning machine in the laboratory. I mean, we discussed about that, how that works. And there we try to do optimal cloning attack to a secure channel, which was about, let's say, less than 10 meters in the channel. And then we try to compare what's going on if you attack to a channel which is two-dimension or three-dimension or four-dimension until seven and see the effect of Eve in the system. And the effect of Eve in the system was errors. So, we will handle, we will introduce errors. And if you go to higher dimension, you will see that the error that you introduce due to the optimal cloning attack to the system, also error will increase. So, for example, for the case of dimension seven, this error was almost close to 37%, 33%. Good. So, that was showing that going to higher dimension will help you to detect the presence of Eve. Okay? And that was very important. I remember at that time these articles received a lot of news media, news attention. And they call me from BBC and they say, which system have you hacked? There is no QKD system that we can hack. There are some prototypes and we hacked that one. They thought that we hacked a government system. Anyway. And remember that also I told you that we should be careful because our detectors, they have a dark hunt. So, there is no perfect detector in the world. So, even if you have a detector in a laboratory, if you read out the electronics, you will see that if you cover the detectors, sometimes the detector starts to click. This comes from noises. Shut noise, thermal noise or whatever. Electronic noise that you have it there. And you have a certain amount of them. So, they are, for example, good detector, they are below 100 count per second. In one second, 100 times they are clicking in the wrong way. You have no idea. Okay? And good detectors, they have really low dark counts. So, that's the reason that in order to get a better detector, you have to call it down as well. So, you have this imperfection in the laboratory. And also, we talk about the generation and detection scheme. Mikhail asked me about the way that you can generate the mode. And we say that if you use special light modulator, usually you are not perfect because this is a phase object. You cannot create an amplitude, also an amplitude and a phase at the same time. Even if you use techniques, these techniques are not perfect. Always you have errors. It's not experiment. It's not theory. In the experiment, always you should handle errors. And even we have a lot of techniques how to clear our data. Okay? So, we have detectors that are clicking in the wrong time. We have generation scheme which they are not perfect. We have detection scheme that they are not perfect. So, we have something in the laboratory that we cannot control. It means that even when you go to higher dimension, you don't win always. Okay? There should be an optimal. On one way, you can handle more error. On the other way, since you have to detect the state, then these detecting of the state depends on the way that you are generating. Depends on the dimensionality of the space. Then all of them, they are playing roles together in such a way that you will get an optimal dimension for a specific QKD system. You can even add AI to it which we are trying to do AI and just to understand if the AI can help us to find an optimal dimension for a QKD system prior to establish a secret channel. Okay? So, that's another point that we have to handle and always we have to be very careful with it. Good. Now, we are entering to the new field. So, now we are talking about quantum channels. So, at the beginning of the presentation today, I mentioned that I miss one part which is the different channels. I want to communicate with you. What are the best ways? Right now, it's easy. It's a voice, right? Pressure goes to your ear and then you can detect it. So, for light, when we are talking, there are different ways that you can do communication. Either you can go with fibers which is waveguide or you can go with free space or going through media, different media. Okay? So, let's go with the first one which is we have spent a lot of money on this which is fiber network and that's a fiber network all around the world connecting different parts of the world, North America to the Europe and also Europe, North America to Asia and that's the network that you will get it. You can get a better image there. So, the most trivial thing is that we can use the fiber network that we have. Good. Let's try to do that. And there are already QKD systems that you can go and buy. One of them is from ID Quantic and you can go and I think I have chosen the best one right now is a Kali's 300 which is a quantum cryptography platform and it's based on a phase modulation. We talk about that. You do the phase modulation. It's qubit again. It's two-dimension and the other side you will detect them and then of course in order to do QKD you are not sacrificing the classical communication. If you remember always I say to you that there is a classical communication. So, the QKD network that will happen one day will be on the top of classical network that we have. Classical network will be used to share the message which is encrypted and QKD system will be used to share the key in such a way that you can read it, okay? And this is node to node. It's two points. It's not a network. If you go with network will be more complicated and here what is happening you can encrypt the data and from the other side which is this scheme you will have right electronics that you can communicate with the encryption schemes and you have the right way to decrypt the scheme and the way that they do is a dark fiber that you have it in underground or in your city. In Otao we have one of those systems. It's in an RCE. Okay? Good. But there is a problem. You cannot go more than 80 kilometers and the maximum rate that you can get is about 10 kilobits per second. Not more than that. So, right now there is a fight between China and United States in technology side. What's the fight about? 5G technology. Because we are going to increase the bandwidth. Why 5G is extremely important for us? Betrayal. Betrayal. What you can do with this betrayal you almost can control everything. Any devices in real time. That's the fight that people are going for. And what we are talking about the QKD schemes is we are talking about 10 kilobits per second. It goes back really to almost 20 years ago. So that's a serious problem that we have. So going to high rate is not feasible. And that's a serious problem. I will come back to this. Now one thing that we were discussing also with a couple of colleagues is having new fiber. It might not be possible but not be feasible essentially to interrupt the infrastructure in the world but one way is that having a fiber which can carry more modes in such a way that you can use the high dimensional QKD benefit that you have. You can increase the bitrates in one way. And this fiber comes from one of my colleagues in Boston that he fabricated in 2013 if I recall well. Yes, in 2013 and this fiber the standard fiber that we have let's call it step function fiber what is happening at the core you have a different refractive index and the cloud you have a different refractive index. And usually depending on the dimension of that you have single mode optical fiber you can have multi-mode optical fiber. Several modes will be supported or only single mode will be supported. Here what they have done if you look at the center at the core you have two regions. One at the center, one at the periphery which they have a different refractive index and this is what you can see. The red curve is for different refractive index. And the blue and dark they are for the modes almost they are matched so in such a way that the intensity is matching with the refractive index. So if you send one of those donut beam inside of this what is happening this donut beam will be propagating without being disturbed. And the modes that they will support and this fiber will support is these modes. Either you have they should carry orbital momentum of absolute value of one it means that they have a donut shape all of them. But they have also different polarization. What is happening if you send these modes inside of the fiber then they propagate without talking to each other. They will not do the crosstalk. They will preserve. It looks like polarization maintaining fiber. Are you familiar with polarization maintaining fiber? How many people are not? Polarization maintaining fiber is indeed when you talk about fiber you have problems with fiber. Some is good. You can transmit pulses. There are several issues that you have. There is no medium that is not dispersive. All of them they are dispersive medium. So if you send pulses what is happening at the end the pulse will be broadened. This is the first problem. The second issue that you have the fiber usually has a tension. Either you bend it you go underground or somewhere else what is happening if you send a certain polarization state after that this looks like a birefringent material the polarization state will rotate or become elliptical. What they do usually they break the symmetry. They make it isotropic by having an anisotropic by having an elliptical cross section. In this way you have one preferred polarization direction and another preferred polarization direction and they have a different group velocity and they don't talk to each other. So we call them polarization maintaining fiber. And here also is the same scenario. What is happening? You break the spatial symmetry in such a way that the fiber only supports those modes. Okay? Good. And we try to use them for QKD and essentially those were the results we created them and how to create these sorts of modes will be a discussion for after the talk I'm sure that some of you may want to know how we can create these sorts of modes. We can create them theoretically. This is the state and by the way there are single photons. Those experiments they were repeated many many many many times. I don't remember maybe for each of those pixels maybe about 100 photons in average I think. And then this is before sending through the fiber and that one is after the fiber that you receive it and this is just to characterize it. But essentially when you do QKD you repeat it only once. You don't do this. This is only for showing to the people and telling them what we are doing really. Okay. And then as usual what you have to do we have to look at the probability density. And we have tried to do it in two dimension for the case of polarization and we can try to do it also with the structure photons what we call it for the two cases. And essentially we were able to get oh there is no cure rate. Here we had about 1% 1.8% error and here it was about 6% error. So steel going to higher dimension will help you. Okay. And a year later a couple of colleagues of mine David David in I think in Finland if I'm not wrong they Denmark sorry they tried to extend these to much higher dimensions. So again what they have you have a classical communication scheme and then you have a QKD system which is you generate the state and from the other side also you detect them and don't go through those details because we all discuss about how to generate them and detect them it's only a matter of details if you want we can discuss about that later on. And finally the state that they have chosen they were those states. So you can go with the state of plus 6, minus 6, plus 7, minus 7 own superposition of those or you can go with different superpositions. What they call the state of phi italic form and zeta and psi. So you have four sets essentially for mutual and biospaces and then you can use them and see if you can increase the dimensionality. And that was the result which is wonderful. The result is that you can as I mentioned if you stay in the same base which is psi then you will see the autogonality between them. If you stay in zeta as well you will get exactly the autogonality and between these two you will get mutual and biospaces. No one really plots them because it's very trivial. You will get 1 divided by 4. And here the same situation and here the same situation. So if you go with two dimensional space you will get about 22, 23 kilobits per second. Okay? So that's what you go with the dimension 2. If you go to higher dimension something like 4 dimension you will get almost 40 kilobits per second. So you can increase essentially the key rate and that's really important by a factor of 2. Okay? If you go with the mix of these two what we call it multiplexing then you can go to almost 20 kilobits per second. Rate is really really important that's the reason that we are pushing in the direction. Good. So that's fiber. But as I say the fibers they have a limit and the limit is dictated by the loss that you have in the fiber. They are not perfect medium so they have losses and after 100 or 200 depending on the type of fibers almost you have no signals. You cannot do anything. And even if you look at those maps you will see that we have something like repeater. It gets a signal, you amplify it and you will send it. This is what we have in the classical communication world. But what we know in the quantum world we cannot have a repeater. We cannot amplify that because we have no cloning turn. We cannot get a signal and send it. So there is a problem here that we have to tackle. How can we resolve this issue? Any idea? Of course I know that senior people they know very well. 60 percent you may. Yesterday we talked about that and I told you yes depending on the dimensionality we can do optimal cloning. No you cannot do that because if it's optimal cloning then maybe someone attack to your system for yourself and sending the other one. And then attack your system if you don't handle the error properly. So essentially for dimension 2 you can go with 83 percent. 17 percent will be errors. But we are monitoring error if it's 17 percent we know that someone is hacking into our system. We don't care that this error is coming from loss or coming from idea imperfection whatever the loss is associated to Eve under any condition. We cannot make 10 copies. Maybe someone is attacking to our system with photo number splitting. No idea guys? Increase intensity. We cannot do that. We cannot do that. I mean if you have more than one photo someone can put a beam splitter taking one of the photo and doing an attack to your system. And if you recall when we say that when I said to you that you can have attenuated laser you can do attenuated laser but the mean value should be really below one. If it's higher than one someone can attack your system. Any ideas? That's another way. So what we can do essentially is building up a quantum repeater. And in order to do so we need to do entanglement swapping and on the top of these what we need we need a quantum memory. So two people, let's say we want to communicate between this place and that place. Okay? Between this place and that place. What we do we create entangled photons between these two sides. Entangled photon between these sides. By the way this is not matched with what I'm saying on the up. I create entangled photon between these two then I will do bell state measurement between these two photons and then these two they will be correlated based on the outcome of that. So if I announce the outcome of these then I know that these two photons they will be correlated. This is the one way that you can extend the correlation to longer distance and longer distance. But what you need here is a quantum memory. And that still is a challenge. Okay? There are activities people they do with nitrogen vacancy atom with other things with a cold atom but still is a problem. Okay? So we are limited to certain range and this range is below 100 km. We can do intercity QKD system we can build it up no problem but for example if I want to communicate to Roma I cannot do that. It's more than 200 km then I have to use something else. What I can use is satellite. So you do communicate with satellite and then you allow satellite to communicate with other parts. Okay? Either you share there are techniques there are different ways you can share the key with satellite and satellite will share it with these parts or satellite will share entangled photons between these two and you let them to be correlated there are two different ways and essentially both ways are working they have drawback and some benefits from the two different schemes either having source up or source down is depending on the schemes that you are going for. Okay? So that's a possibility that we can extend the QKD system a QKD link or much longer distance. So I'm sure that you heard about this is from a group in China they launched a satellite and they were able to do QKD between ground to satellite or satellite to ground and the schemes that they have it is exactly based on the polarization way and they were able to share a key and again the key was limited to few kilobytes per second not more than that and then what they have done they share a key with satellite and then satellite with another place from China to a place in Austria and then they were able to extend the link to much longer distance so essentially with the fiber for example that what is happening even if you go to fiber you can reach to one tenth of this even not longer than this distance so this is the way that you can extend the QKD system to much longer one in Italy also in Padova Pino Valone one of my colleagues Giuseppe or Pino we call him also they have done with one of those satellite that is on the orbit low range one maybe the distance I don't recall maybe it was about 1000 kilometers if I remember something was about 1000 what they have done they went to an observatory and they installed their system there but it was a powerful laser and they send the pulse there and inside of the satellite what they had they had one of those cube mirrors okay do you know what is cube mirrors anyone doesn't know so cube mirrors those cube corner mirrors let's say the simplest way is you have the corner that we have in somewhere one of those sharp corners so take this paper assuming that inside of this is made of mirror when you shine the light on the top of this it goes back in the same direction okay is a simple mathematical question that you can solve it so you have cube mirrors installed there and what they have done they shoot the laser on top of this of course the beam is getting bigger it will diverge but the portion of that hits the satellite and reflects back and with the telescope they catch this portion and they were able to send the pulse and receiving it back and then analyzing it so they were able to send a key essentially to themselves but you can say that the earth is moving around so you can say that is a different place when you send it and you receive it and of course they have seen very very interesting phenomena like a relativistic effect as well because this satellite is moving you will see the Doppler shift as well and some very interesting effects and you can handle it properly in Japan also they have a program for launching a satellite I don't know maybe they are micro-satellites it's a small dimension not micro, it's like a centimeter but it's not a small one and it's not a big one and in Canada also we have a program which Tomas Yanovani is leading and is a QSAT and the aim is to launching it in 2022 something in about two years from now so all of those they require to be tested in a free space so before even launching and trying to do QKD with satellite what you have to do, you have to try it between two ground bases but you have to send the signal on the free space so these are what people in Canary Island it was 134 kilometers if I recall well 143 kilometers you can send photons from one side to another side but in this experiment they did quantum entanglement swapping so they share entanglement between two parts I will talk about the details of this but I want to give an overview I don't want to talk only about my work but some of my colleagues work and this is another experiment that they have performed I think they have performed teleportation between the two islands and you can create entangled photons to pair of that and then you can do the teleportation between two places good so I will tell you more details about that because when we do it by ourselves we know more issues than the setup of other colleagues in Ottawa also we have tried these to perform QKD between two buildings but our goal was not really sending lasers we want to really send single photon from SPDC and moreover doing high dimensional QKD and see if the high dimensional will give you a benefit or not it was extremely extremely difficult to do the experiment I will tell you why if you want to do this sort of experiment first of all you have to communicate with the airport you are not allowed to go to the roof and do the experiment if you have a laser pointer shooting to the sky you may be in trouble you are not allowed to go higher than three degrees out of horizon if you are going higher than that they may catch you and you may be guilty this is a serious issue second on the back of these two buildings we have to communicate with both in such a way that the sniper will not kill us there were a lot of other issues in terms of safety and security no one really allows to go to the roof because maybe if someone has a health issue maybe a suicide will happen and then you will be guilty of those stuff so there were a lot of admin stuff and students what they have done and this project just for you how many of you are undergraduate students one only one an undergraduate student of mine lead this project so Alicia lead this project and at that time she was an undergraduate student with Frederic Bouchard, Robert Fickler which he came from Anton Zydigar group to my team as a postdoc he was an undergraduate student as well and they tried to build up shed in Canada it is extremely difficult to work outside it sometimes gets extremely cold they built up shed and they brought all of the equipment outside of the roof and they tried to do QKD we have tried this twice going to Germany we brought the entire of our equipment to Max Planck because they had a link there we tried to go there and perform the experiment we were not able to do that and realized later on why not all experiment at the first glance, at the first trial they will work you learn by time and this project was I think four or five years long and it takes a lot of time just to learn and step by step we understand what are these sort of problems good so and our goal was to go to higher dimensions and using single photon case how many of you are experimentalist okay how many of you work with the single mode optical fibers is it easy to align single mode optical fibers tell me loudly not at all because you have to couple to a single mode optical fiber which the dimension is about five micron what they have done they send light through a telescope to the other side and they couple it to a single mode optical fiber over the distance of 300 meters even in laboratory is not easy to do that and the goal was going with higher dimensions I'm showing you the polarization pattern of them and I will talk about them after the discussion that we will have I will tell you how to generate those modes but if I don't have my my telescope to see the polarization my lenses to see the polarization all of them they have the same intensity shape if I send a single photon if you don't have polarization analyzer what you will see you will see a uniform intensity distribution so they are identical so no one can really watch and tell you what are the states and these two they are mutually ambi-spaces set projection of those there will be difference I will tell you in the next slide and here what they have they use this non-linear crystal that we discussed previously you pump a crystal which is periodically pulled crystal KDP crystal and they can get entangle photons but we don't need entanglement for QKD in general you don't need entanglement unless you want to do entanglement swapping which is a different scenario you want to go with protocols that you need entangle sources here what we want to do we want to make sure that we are creating single photon we are not creating more than single photon and we keep one of them as a target for ourselves just to tell us what is the GPS that you have essentially the current link that we have I will talk about that as well and the other one we will keep it as a signal what we do we encode the information we encode one of those we switch between these two and we choose one of those bases and we combine them on a dichroic mirror so the signal and the target which has the information about the time they will go through the same link and then finally we have a mirror image of that there will be signal and target they will be splitted from each other with a dichroic mirror because they have a little bit different wavelength target goes to a single mode optical fiber and the signal goes to a detection scheme which is choosing between these two and projecting them good is it clear so what is happening we have turbulence between these two I will talk about turbulence effect what is happening between these two let's say building they are vibrating right there is a possibility or the air between them is not uniform in terms of temperature so there is a current a flow there so the beam sometimes will not be coupled to this will not be coupled to single mode optical fiber yes absolutely we have done that only because we want to monitor the turbulence no I told you from the beginning I do not need entangled photons I created these in such a way that I know a trigger I am heralding it and I am using the heraldic photon to monitor the turbulence not necessary look those entangled photons they are coupled to single mode optical fiber and the entanglement was in the spatial mode and after coupling to single mode optical fiber they were erased so you will get a product state you will not get entangled one and then sometimes the turbulence is freezed then that will be coupled to single mode optical fiber and then I know that the signal that I have it here is the right one and I will collect them we have tried to do this in two different regimes and it was for you if you want to know about the setup that was the setup Alicia and Robert they were enjoying performing the experiment there ok so those two states those two mobs if you look at them the projection of these on these will be 1 divided by 4 projection of these on that will be 1 divided by 4 you can do the mathematical calculation but even you can see that the polarization orientation is orthogonal to that one like exactly at the angle of I think 90 degrees so this is this is H polarization and this is V polarization so they are orthogonal and here the same scenario they will be orthogonal but in some other regions they will be parallel then you will get 1 divided by 4 if you do the measurement as well in the laboratory each of those they are orthogonal to each other so if I have this mode and I want to detect them the probability will be 1, the rest will be 0 so they are really mutually ambide spaces and those are the theoretical one that you expect if you are in the state of Psi if you project it on Psi you will get 100% probability of detecting them if you are detecting them in a wrong base and the same scenario for the other case good and that's an example that this was what we have performed in the laboratory in the distance of 5 meters what we get was this and this was in the free space link in the distance of 300 meters and we were able to send the message of parliament to the other side and encrypting them that was the encrypted one and then we were able to send the key and decrypting the message and that happens I think in a second something like that then we want to talk about the benefits why we are doing that we can do that with the polarization if you do it with polarization you will get this density probability if you do for 4 dimension what you will get you will get of course higher key rate but sometimes what is happening in the 2 dimension due to the turbulence there is no one hacking your system but the effect of the turbulence will be noises it will introduce noise to your system in the dimension 2 sometimes you have 11% error and one night for example we had exactly 11% error then we were not able to use 2 dimensional encryption we had to go to the 4 dimensional encoding schemes and this was exactly what we were expecting so if we look at that you will see that in the case of 2 dimensional sometimes you will get low error in this case you will get about 0.43 bits sorry 0.5% error here but sometimes happens then we had about 11% error we were not able to use the 2 dimensional but we went to 4 dimensional case for example we pick 11% error in the case of 4 dimensional and still we were able to establish a key which was even higher than the best case of the 2 dimensional way and that was extremely important for us just I will repeat myself again in the 2 dimensional case the best scenario we had about 5% error in the free space we were able to send 0.43 bits per sifted photon but when we reached to 11% we were not able to send a positive key but when we moved to the 4 dimension we were able even at 11% error to send a bitrate which was higher than the best case of the dimension 2 and that was extremely important for people ok and that's a measurement that was shown to you good right now we have a much longer distance the distance is about 5.4 km between National Research Council of Canada and University of Ottawa and people they built up 2 sheds and inside the sheds we have optical tables which is isolated from the building both sides and even you can see it on the google map I didn't notice that until very recently if you go to the google map you will see that and the sheds are there and the optical tables are there and then they install telescopes and single photon detectors and also single photon source and they send signals from one side to another side and that was the first try that we did it was 300 meters in that short range we are trying to extend it so we are going to build a hotel which will be another 4 km far away and we want to build a network moreover we have I told you about ID Quantic system which we have in university in NRC the ID Quantic network also is there and we want to build up a quantum internet or the city and then also the next goal will be linking to other cities of Canada good briefly I talk about the turbulence my students they went there almost 2 years ago and they tried to send pulses to send photons and detect them and what they have seen is an interesting phenomena which we know very well is turbulence I think Van Gogh has seen turbulence previously so what is happening what is the effect of the turbulence you have air and the density of air is not uniform why? absolutely because we have different temperature the density of the molecules in a certain volume is changing upon the time when the density is changing it means that the refractive index also is changing so if the refractive index is changing the light will be affected by that so if you send which is a perfect Gaussian what I have it in with this laser pointer if it goes through the air you will see different current or different cells that essentially the turbulence is changing there we call it fried cell and you have a diameter for them you cannot send a beam which is smaller than a certain value then it will be diffracted by those cells and at the end what you will see you will see some pattern which is distorted and we did that I mean we tried this and we measured what is the fried parameter that we have and each turbulence has a characterization has a number that will tell you if you are in the strong turbulence regime or you are in the middle or low turbulence regime and with this technique you should compensate for good so we know that if you send signals and the other side you have a beam which is completely distorted this might not be important for the people that they are working with polarization because polarization is almost the same everywhere but for us which we are working with the beam profile this is extremely important because the information is not is not only in the polarization but also is in the special mode good then what you have to do you have to compensate for and the compensation is a technique that astronomers they know very well and they call it adaptive optic system so you have this distorted beam you send it to a system the system has a beam splitter you will analyze what is going on with the wave front of the beam what is happening the distortion is essentially is in phase if you look at the phase but the phase is distorted and has a certain wave front which is changing upon the time in the time of t equal to 0 is that maybe in the time of t equal to t1 is different way, completely different so you send it to a wave front sensor this wave front sensor what it does it decomposes this mode in certain complete basis of the phase and we call those Zernike polynomials okay how many people they know what Zernike polynomials how many people they do know good so what is happening I have an aperture as I said to you why we love orbitangumentum because every optics that we have in the laboratory is cylindrical symmetry if they were rectangular I love helmet Gaussian modes in your laboratory everything is cylindrical symmetry that's the reason that we work with this and all of those apertures they have a certain dimension right they have a certain dimension we call it usually numerical aperture if you want to define based on far field or just the diameter of your lenses you can call it if you have these the diameter usually is about 1 inch right most of us we are working with 1 inch diameter not 2 inches even then you say that what are the possible phases that I can have in this circle in this in this circle how many possible phases can I get and they form complete it means that any phases they can be expanded in terms of those the first one is planner phase right the other one is tilted in this direction wrong X the other one is tilted along Y right we call those Zernicka polynomial Zernicka phases that you need it and they use it for microscopy and Zernicka for this reason got another price okay and then is not only cases you can have astigmatism you can have lensing all of them they are the Zernicka coefficient that you need it okay here what it does the wave front sensor will detect the pulses give it to a fast computing platform and this fast computer what it does it decompose it in the Zernicka polynomial in real time and then in the fraction of millisecond all of them should be done in really below millisecond and we are talking about pixels a lot of pixels that you have to do the calculation and it tells to a deformable mirror which they are extremely precise to move in nanometer regime going up and down and correct for that wave front so they understand what is the wave front is like that it maps exactly the invert of what you have it here on the wave front of this then the wave front will be planar we call this adaptive optic system and it will tell you only building up that for us will take a company very expert company almost more than a year okay and I'm showing you only the supercomputer that comes with this is a supercomputer that you needed to do this sort of fast computation is the size of Alicia almost good so in order to do so in order to compensate for turbulence you have to do this for almost two years you have to optimize it in the laboratory and then you have to bring it to outside of the lab so I will give you let me see if I have something else yes I will give you about 10 minutes as a break is that fine and after that we will go with a different regime the distance is long but it is not sure so let's start there were a couple of very good questions and I would say I will just address them right now one of them was about the Doppler shift and Mikhail asking me the Doppler shift will be small but you know there is serious point of view I would say serious opinion of physicists usually when you go to laboratory you will get a curve right if there is a bump here physicists they spend about years just to understand why there is some data like that and there is a bump here and it is really really serious I will encourage you to look for the first second harmonic generation in the world and the paper was published in PR at that time and there is an image and the image supposed to be a set up you know a diagram and finally there was a dot here and the dot was experimental result and editor erased that because he told that this is a mistake it's just in the printing issue anyway so we care about the details that is something we really care about that and Doppler shift even in this case because the satellite is moving transverse is not moving towards you is a transverse Doppler shift but still plays a role and if you look at the paper of Pino they considered that and even from this they calculated how long they can send the pulse there and coming back so those details are really important for us where are we good the second question was why we are trying to do QKD between distance of 5 km why at all we are going for fiber let me go to one of the slides I think I tried, I told that I was clear after distance of after distance of 200 km almost you don't get any signals is noise 200 km means something here with the fiber you can only reach here if you want to go even longer what you need to do you need to have a quantum memory and entanglement swapping and then distributing to longer longer distance but what we are talking about we are talking about 7600 km this range you can share the key with the satellite and satellite shares the key with distance this is the reason that we go with satellite and one of your colleagues he asked me why essentially we are going with satellite because the loss is really low compared to the fiber you can go to even 1000 km even 2000 km and loss will be extremely low and one other thing is that when you go higher and higher the density of air will reduce as well so that's the reason that we go with 5 km distance 5 km on horizon is identical to sending the light to satellite these exact turbulence the same turbulence essentially yes, your question from environment that comes back to better detector, better filter you isolate them and moreover I did not say that most of them they are synchronized by GPS so we synchronize them we have a GPS clock they tick in the right time and we know where the signal is sent and we should look at that signal those are all details there were another question you are not sending here it's shared with satellite and satellite shares with this you need to share a key once it's one pad you share the key with the satellite and the satellite shares the key between this A with B, B with C and then B and C they have the same key yes, they do that and some other satellites as we discussed they have entangled pairs they go down you have entangled photons of A and B then these two they perform measurements and then they follow the protocols that we have and then they have the shared key no, they should be in the same view satellite sees both of them if you go to a higher distance then you can see really wide range and you can share between the two points which you cannot reach it for example, for Canada you can go from coast to coast easily with one satellite and this is the target that we are going for no, it can go to higher the satellite depends on the satellite that you are launching it can be low orbit or it can be higher orbit or you go higher I don't know really the details of that is the Canadian Space Agency that they are working on this but for example, for Canadian one we cannot try to go to coast to coast essentially I should say coast to coast to coast okay, but I know that Saint John we are trying to connect it to Calgary and that's a goal and of course it goes through certain orbits, Ottawa and Toronto they will be connected and Saint John as well so it depends really on the way that the satellite is designed which orbit it should go but it is possible it is a feasibility I don't know about the current one I have no idea honestly I don't have knowledge about this but we are trying to go to visible because we have a better detector we have better can you hear me, better detector good, there was another question someone else asking me a question this was all, okay yes previous slide should be this one yes, no this one is really powerful laser is a powerful laser, is not single photo no, is not quantum okay we were here, okay so we talk about satellite to ground and we talk about the fiber which is inside the city and we are trying to do it with drones in Ottawa ground to drone but also we know that 70% of the earth is made of water and we have submarines everywhere so this is another channel though I don't like it but it is a fact that sometimes you need to do the communication with submarines or submersible if you want to be peaceful by the way also submarines they have a lot of applications for monitoring plastics this is a big project that we have in Ottawa in Canada that they are looking for resources of plastic and measuring those plastic the dimension of those plastic and that should be transmitted in real time and then they do inverse problem solving and they understand where those plastic are coming from so they have to take all of those information so submarines communication with submarines sometimes is extremely useful even for peaceful application okay and we realize that there is interest in quantum communication our communication with submarines our underwater channel then my students they decided to go outside and they started to perform experiment in a swimming pool this is not my home swimming pool it is a swimming pool of one of my students parents so they were there for almost 2-3 weeks they built up the setup there they had another setup there and of course they had a gazebo and they were enjoying there they had beer and barbecue as well and by the way this was we took this photo and this photo is published with the article because editor could not believe that we have performed this experiment in outdoor condition so they brought there and the ladder is just there for the classical channel it is not quantum it is nothing really the data will be transmitted it is chosen only for classical channel we could have a wire going from another place but we just installed there then you have two prescopes one is going inside I mean is a prescope configuration goes inside and then underwater you have a communication and then it goes back up and you do the detection system and let me show if I have let me see if I have something else to show you that the setup from the single photo side is inside of the box for the laser safety propose you have to keep it in the box and then you send the signal and either photo there and finally you need someone of course to do the most of the work which is doing the alignment he was undergraduate student as well at that time I think he was having fun Felix and then finally they had beer and they tried to do communication between Alice Alicia and this is a classical communication by the way and Azad which he also has a cell phone and they are trying to do counter communication and you know who is doing the most of the job which is Felix ok and what they did they tried to send only special modes and just to see what's going on with this and the distance was not too long 5 meters not more than that and the single photo was sent to water and the wavelength was 7 10 nanometer and just to tell you water is not transparent at the visible you know that the maximum distance that you can see is something about 5 meters not more than that you cannot go lower than this but water is almost transparent at the UV and green wavelength between 350 to almost 500 water is transparent the range that you can transmit information or you can transmit pulses is about 200 meters ok I mean yesterday I mentioned that the infrared will not pass so it goes only with a certain thickness which is about let's say 200 micrometers this because it's water ok if you send UV or Hini laser through water it goes to a certain range we could not go to the wavelength of 400 or 500 nanometers because we could not push the SPDC to go to that regime and that was a technical problem that we had but still we want to show to the people that you can do QKD even in underwater channel good again single photon SLM this time we used SLM special light modulator we encoded the information there and then we pass it through water and then we detect them and we had our GPS clock again and those are the results and this is for classical beam I'm sending a Hini yes because it's a non degenerate case this one is 910 we try to push it down as much as we can we want to have one of them going to more blue the other one we don't care because the other one was transmitted through the fiber and fiber is ok with telecom wavelength this is what we have done good point so this is the pulse that we sent it was a Hini pulse is not information there we just want to check out what's going on with water because essentially you have to work at the single photon regime you are not working with a powerful laser as our colleague mentioned so if you send this this is the outcome after 5 meters it's unbelievable isn't the beam is dancing in a strange way so the turbulence here is very very different from the turbulence that you have it in air in air the speed is extremely high is about more than 300 hertz that's the reason that all computation should be done in fraction of millisecond else you cannot compensate for but here the speed you can see it even with eyes is less than 100 less than 10 hertz and that's the first thing and second you will see that the turbulence is not look like free space in another perspective in the free space the turbulence cause you only tip tilt up and down that's all here you have some sort of astigmatism which is new and we have never faced this previously so the beam is changing completely it means that information if you send information in special mode will be completely lost and we sent one of those OEM carrying beam the beam that carries orbit and momentum exponentially do you remember that those beams they had a phase singularity right so the beam was if you remember it was exponential of I L phi and we say that L is equal to 0 it will be planar L equal to 1 it means that if this is phi equal to 0 then the phase will be 0 if phi for L equal to 1 then if phi is pi divided by 2 then the phase will be pi divided by 2 here will be pi 3 pi divided by 2 so that was the phase at the center we had a singularity because the phase was undefined for L equal to 2 what do you have you have 0 here you have pi because it's changing with 2 twice of the phase twice of the polar coordinate angle and here this becomes 2 pi and here becomes 3 pi and between them will be pi divided by 2 3 pi divided by 2 and etc and again at the center you have a phase singularity we sent one of those beams this one L equal to 2 I am sending L equal to 2 what is happening with L equal to 2 these L equal to 2 will split out in a beam with 2 singularities essentially the singularity here 1 is unstable it becomes 2 the total is conserved but is very unstable so this one it becomes if I watch the phase here because it will be a stigmatism it will be 0 pi divided by 2 pi 3 pi divided by 2 and etc and here the same scenario you can calculate that it will be 3 pi divided by 2 start from this here it will be pi 2 pi here it will be pi divided by 2 here it will be pi orientation is important how it is changing 0 to pi 0 to pi is the same way so what happens that the singularity will split out and it becomes 2 singularities and if you probe it upon the time you will see that the singularities they are moving around with the turbulence and there is a consequence of the turbulence that you have it here and you don't see that in free space propagation in the air you don't see these sort of things if you go with L equal to t what you will see it becomes 2 singularities and they are moving around this means that they are changing so what we have to do then we have to look at the cross talk between the modes and that was the cross talk between the modes you send L equal to 0 you will detect L equal to 0 is almost there very rarely goes to the other rest it goes but a little bit L equal to 1 ah the cross talk increases you will see that it is more look like brighter more look like blue if you go with L equal to 2 you will see that ah the rest is exciting so what is happening there will be a cross talk between the mode that you are sending and the mode that you are detecting so that's a problem that you will see here so that defines that which dimension you can do QKD with it you are not allowed to use dimension 7 but you are restricted to the dimension 2 dimension 3 dimension 4 that you will see in few minutes first of all you have to characterize the turbulence again and this is what we have done and you have to decompose those modes in terms of zernicapolonomial that previously we discussed about that so you have a flat face you have tip tilt the color coding is look like the wave front is tilted in this way or that way this is what you see y direction or tilted along x direction or you have astigmatism which is some sort of lensing either the beam is focusing which is this one or you have some sort of astigmatism the beam is moving into the opposite directions up and down this is what you will see ok and you will see that in water in air you have only these two three terms in water you have adage terms as well you have zernicapolonomial 2-2 and 2 plus 2 that shows that there is a cross talk between the modes and essentially if you do you try to do QKD in dimension 2 this will be the result you will have about 6.5% of quantum bit error rate if you do this is a theory just to show to you and that is the experimental result that you have it for two different mutually unbiased basis that we talk in OM basis you can do different protocol which we call tomography protocol you don't go with only let's say HV is not HV by the way here is orbitangumentum but just to tell you if you do with HV antidiagonal diagonal also you have to do left and right polarization so you have to go with other set of generators that you have eigenstate of the generators let's say 2-2 this will be superposition of 2-2 with plus and minus sign and here it will be with plus i-i and you will see the probability density matrix that you see this for dimension 2 we try it also for the dimension 3 and dimension 4 dimension 3 worked but the dimension 4 did not work at all so that one did not give us a positive key rate only dimension 3 worked so that was a restriction that we had without compensation for the turbulence we could not use the benefit of high dimensionality good and that was a key rate last summer not this summer a summer before also my students they love to go outside they have no idea why they rent a cottage in the river of Ottawa this is Ottawa and it's almost about 2 hours of drive I know very well because for 2 weeks it was my job each day driving there and coming back and they rent a cottage there in a lake and they try to do QKD there on the realistic condition why we are trying to do this because there are some things which we have no clue when we are working in the laboratory one of the easy things that I saw in the first night which I will never forget and I learned very very quickly and we tried to find a way to solve it is that you have a condensation almost everywhere you know what's condensation you have you have a vapor of water everywhere right and when you have a mirror the water starts to stick on the mirror and then immediately you have no light after 2 hours of working we realize that there is no light coming to our side and I told that one of the students that she was in the water swimming and trying to align the setup I told that she did misalignment and we spent about the entire night one by one going back and finding out what's the problem and finally we realized that the problem is just a mirror before the laser after the laser the mirror is full of water with the condensed water condensation happens only there and we realized that you need special optics to perform this sort of experiment and this is something that you don't learn in the laboratory unless you go outside you face it and you will learn these sort of things they render cottage there and they try to perform experiment I do have photos of them but I don't have a right to show it to you anyway and they were not lucky because they were rained a lot during that summer and just a couple of days so the water was not clean the water was full of algae dust and scattered the light in a terrible way and they try to do simple QKD protocols with that and this time we did it with UV light and we tried to change our protocol from single photon regime to attenuated henie laser that was henie laser, attenuated diode laser and that was the result of simple polarization QKD and we were able to establish a key but what we have seen also again here was turbulence we tried with the special mode to send more modes you will see that if you send Gaussian modes this is what you expected to send the Gaussian modes after the time of t equals 0 after 5 meters it becomes like this shape in the one second hour later it goes to somewhere else 2 seconds there and finally in the 6 seconds you will see that it goes like this if you send special mode you will see that due to the astigmatism that you have it it changes completely in a different way so we learned that for the underwater QKD we have to be extremely, extremely careful and this was also again characterization of the Zernicka polynomial and we tried to develop a code to do the compensation and this code for those people there are I think a lady she is working she is trying to teach to undergraduate students that an undergraduate student from a genius undergraduate student from high school that he came in and he wrote the code for us and the code was used to compensate for the turbulence and finally that will be the last part of my talk we brought these during winter we cannot go to lake we cannot go to the ocean to perform the experiment we tried to simulate these in a flume in National Research Council of Canada which is jointly we are working together on this and we had a trail in such a way that we can change the distance between Bob and Alice and see if we can have a QKD system for a certain distance we tried this and I have a photo which I want to show you also about the setup here which people they covered the flume because the flume was again extremely dirty those flume they are used to simulate what is going on with a wave from the ocean what it will be the effect of the waves on the cities or other different places around it so and this was filled out with water from the city so it was approximately good example for simulating and then again Alisha tried to do send pulses she sends two lasers one of them is a target beam the other one is the pulse that carries information and if we look at the color of the laser it is very strange it is green blueish so it is the two pulse of green and blue and you will see that the green will be observed very quickly and blue goes to a longer distance so that is the transparent window of water here what we try we try to go with polarization because we know that polarization will not be affected due to the previous experiment we try to go with the special mode which the special mode has polarization and the phase information we try with these two modes which is radial and azimuthal beam and just to tell you radial and azimuthal beam if you put a polarizer at the front of this if you put a polarizer at the front of radial beam you will see such a pattern if you rotate the polarizer to be H you will see this pattern if you go to anti-diagonal you will see this pattern if you go with diagonal this pattern see how positioned this now if I do the Stokes measurement in the standard way I find this state to be totally mixed because in the Stokes measurement I have to do the intensity of H minus intensity of V and if you look at the intensity they are identical they will be zero for anti-diagonal diagonal they will be identical for see how positioned left and right they will be identical so Stokes measurements they will give you totally mixed state but essentially in order to understand the beam you have to do the polarization tomography as well point by point you should have a camera to do a Stokes measurement for each pixel and then plotting them together if you do so you will find out exactly that pattern and these are the experimental results not bad and if you plot them together those are the beams that were we expected so if you send I'm just plotting one of the mobs if you send one of the beams if you send a radial polarized light beam after one meter it becomes like this after five meters it becomes like this after ten meters it becomes like this ok and you will see that the polarization states is almost the same for all of them though in some regions due to the astigmatum gain the beam will be distorted then they try to see if we were able to send certain states and we can do we can establish a key rate and that was the result that they were able to reach they were able to reach to almost 30 meters length and they could send about 0.1 megabit per second which is extremely good ok and for the case of vector modes they were able to send something about 1 megabit per second but for the range of ten meters this is sufficient for people that they are working with submarines because submarines if they want to do communication they have to come to the surface of water and doing the communication with satellite this is sufficient if you go only 30 meters below the surface they will not be detected but they can do communication with satellite or they can do communication with drones or planes and this is extremely important in the rate of megabit per second right now the communication in submarines they are done with a kilobit per second and is done with acoustic way is not secure at all so I will go to end of my talk just to tell you that structured light is extremely important it sends you more information you can go with different maps of course going to higher dimension is beneficial for you and of course you can reach to a very very very sophisticated topological structures and by the way this is made by one of my students wife the cupcakes you can handle more errors you can send more information you can try to do different channels and our goal is to build up a network and that's the reason that we are trying a lot in Canada to build up a quantum internet and that will be a work between 20 groups in Canada I should thank the agencies including Canada Research Chair the position that I have from Prime Minister Office and National Research Council of Canada they helped us a lot including Max Planck I learn a lot from Max Planck people and they allow us to perform the experiment there at the first trial although I am a junk there Canada Foundation innovation those equipment they are extremely extremely expensive so you have to spend a lot of money and invest a lot just to change a little bit of knowledge that you have European Commission as well and also Canada first excellent research fund which is from University of Waterloo that I am receiving money from them and also my team some of them they have already gone Fred he leads most of the underwater QKD and also optimal cloning machine hacking and he is right now a researcher in National Research Council of Canada Robert Fickler that he tried to he supervised and tried to perform the free space QKD he came from Anton Zeilinger group right now he is a professor in Finland Hugo Laroc which he works on the electron beam but I didn't talk about the electron beam at all and also a nut theory he is right now a PhD student in M.R.T Eliyahu Kohen which he was a student of Yakir Aharov he came to my group as a postdoc and we have performed a lot of ghost imaging techniques and instruction free measurements in such a way that you can detect objects without eliminating them and right now he is a professor in Bariland University Ingwen Zhang he works on interaction free and also all of those quantum sources he is right now a researcher in M.R.T he is a smart high school student that I mentioned to you he wrote the code for us genius person and right now also I have some other students which they left I had Sergei which he came from Maxpang he is a researcher in a company Alicia is there for QKD Fatima also did fiber QKD as well Felix underwater QKD and right now he is working on compress sensing Florence also she worked a lot on the underwater QKD and right now she is trying to build up a quantum microscope whom else Kevin is working on the software QKD you need a lot of software I didn't talk about that at all you have to really build up a classical communication first it should be written by yourself and then build up a quantum network on the top of this so he is working on the electronic of this do I have anyone else we are also working on the satellite to satellite communication and I think that is all my collaborators so this is not a work of one single person it is not only a single group it is all around the world that we are collaborating and we are trying to transfer knowledge to each other and learning from each other it starts from Gerd, Miles, Bob Boyd, Paol Korkom Rafal, Yuval, Yakira Harnov as well and which is right now we are working on doing quantum encryption but in a different fashion she is at the University of Ottawa as well Khabad Khabad is I would say my right hand at the University of Ottawa he is working at National Research Council but she graduated from your team right Bahid, from Professor Karima Purs group and he is really helping me a lot on the theoretical side Kristof as well I learned a lot from him from Max Planck Jeff Landin as well maybe you are familiar with his work on measuring the wave function of photon and seed art ok so with this I finish my presentation and now I am open for one hour for questions I reveal the questions