Correcting noise in optical fibers via dynamic decoupling
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Correcting noise in optical fibers via dynamic decoupling

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CC Attribution  NonCommercial  NoDerivatives 3.0 Germany:
You are free to use, copy, distribute and transmit the work or content in unchanged form for any legal and noncommercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor. 
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2011

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English

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Abstract 
One of the major challenges in quantum computation has been to preserve the coherence of a quantum system against dephasing effects of the environment. The information stored in photon polarization, for example, is immediately lost due to such dephasing and it is crucial to preserve the input states when one tries to transmit quantum information encoded in the photons through some communication channel. We simulate random birefringent noise along realistic lengths of optical fiber and study preservation of polarization qubits through such fibers enhanced with CarrPurcellMeiboomGill (CPMG) dynamical decoupling. The sequence, implemented with waveplates along the birefringent fiber, helps to maintain very high fidelity over a given length of the fiber. Moreover, errors arising due to the timedependent control pulses can be completely eliminated as here one only needs to incorporate the wave plates in the prescribed way. This simple and fairly practical model is valid for preserving any general polarization state of the single photons besides providing a direction towards achieving scalable and useful quantum computation with photonic qubits.

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00:00
people alright so let's not go for the session is correcting noise in optical fibers here than a weak coupling given by Kathryn Brown and Kay thank you very much fairer conference organizers for letting me give a talk as you can tell from my accent have come from Louisiana and I thought I have been given told them and a lot of PhD students Bosco menisci are former postdocs Peter is now a study but in New York currently and not to Professors Kwong Lee and Jonathan Dowling I'm gonna be talking about correcting for the parallelization of of a photon in an optical fiber and with the workers simulations rather than analytical so but begin with an introduction are then introduce and dynamical the coupling again I know you've had several introductions this week but 1 more can't hurt I then introduce the CPNT he's the 1 we're using and finally show our results and then some conclusions and so dynamical a coupling is some type of open the quantum errorcorrection is no can replace the closedloop errorcorrection protocols that we've been discussing last day such as servers carried the hope is to introduce it and the full we perform these operations get the areas down to a suitable level for threshhold looks at the moment most of and the areas set in transportation and moving gates far too high for threshold level and we can't even begin to think about forming a quantum error correcting codes the several forms this openly quantum error correction and dynamic the couplings 1 example in the other 1 which I think you hear about its decay inherits the subspaces
01:53
and so this in Kuala previous work done on using dynamic the coupling to correct for errors a Tolme's will lie down I did and some key work on proving that you could use then and the coupling to correct for the Prize right and phrasing in optical fibers that was some analytical work driving worstcase scenarios using regularly posts scheme and other work has looked at correcting for mode dispersion in optical fibers and interestingly experimentally there's been work done looking and act photons in being cavities is a different scenario to the optical fibers that that he demonstrated the effects of or the effectiveness of dynamical the coupling for photos and so we're going to consider sending a photon through an optical fiber for to particular reasons amount to do this 1 would be for distribution quantum computing and in that case you wanting to send a general states in the HP basis and the other reason maybe for quantum cryptography and that's slightly simpler the to send a 0 a 1 and your plus minus state so you don't necessarily have to correct for all states and we're gonna model or noise as being changes in the buyer into the fight that caused by changes in the environment the fiber in these changes are gonna happen on the orders of tens of meters and because we're using a parallelization maintaining 5 when you can be correcting for depolarization in the phasing in 1 direction and asking the other direction so that's the standard model of noise that's been being used throughout most these did not meet the coupling talks honest slightly simpler than the more general model and so defacing can be seen as being a rotation around the zaxis of the Bloch sphere and as a result of this we can see that these theory and the 1 state Our put can only acquired labor phase factor and therefore don't need any correction tool that perfect in many other states will gain an error which means that take madam blocks the simplest example dynamic coupling again is even had this week is the spin and spin it so we're
04:11
gonna introduce slightly different diagram from the runners which also gives an idea intuitively of why this works the diagram made with considering that in our state evolve under the the phasing any evolve around the zaxis about blocks there for a set amount of time daily in the diagram the we then form of high posts this reflects the few methods can be thing information made from this state to the states and c we allow it to it and continue rotating around the block sphere said defacing for the same amount time is a diagram right and influence and this continues to coal Prady facing but now defacing is moving state back to its initial position is beginning to actually correct and finally the last 5 holes and brings us back to our initial state and said different forms of dynamic would coupling a useful for different purposes so we've all heard about the URI dynamic with a coupling being the optimal pulse separation but that were we did some initial simulations on that's and we didn't get very positive results and the reason for that is because it works better when the noise is the shop highfrequency Kassoff which we don't have been on noise model so instead we moved on and looked at the CPNT sequence and partner might be lot of might be Mengele and instead using regularly spaced pulses we use the sequence where with placing along an optical fiber so now been going to distance instead of time off fiber firms particles is placed distance out into the fiber the 2nd part poses a distance to out the 3rd 1 a distance out both 1 another distance element to out again and that repetitions of the sequence throughout the 5 back 1 advantage to this sequence is it's supposed to be resistant to errors it within 3 in a way place we sent through a plus or minus states and and the rest this paper by Morton it's we have unincorporated areas into our way place yeah that's something we hope to do in later work in the 2 C 2 gets quite good idea how to do that yesterday so we're hoping to cooperate that in the next few months waiting so we modeled off 5 here as regions of constant by refringens given by delta N. and that delta N. is a constant here not the changing buyer fringes and for constant noise regions delta L and these delta l here at 1 2 3 4 5 we have more than 5 enough data model are actually different let's so the idea is that it's so we have to accept the mean of this distance in standard deviation so the idea is you got your 5 and not the length of each region across by refringens is fluctuating and you don't have to know how long it is and this this is trying to get more physical model and the BIO fringes here we set with some parameters and we set to 0 mean and we set standard deviations as you see in graph so you a median of and after having set median we get if you make this noise given here and that's for 1 region and then we run our simulations by sending a photon on through several regions generating this delta L and if delta N. parameter at random given our constraints each time a new man this well several hundred simulations and then today the graphs that will see 1 key thing about graphs is left to the fidelity the plus states we justify this by saying it's the worst and fidelity possible given that we have no errors on our way play and the reason can be seen that is if we consider sending singlephoton a fiber with a collective defacing of feature which is the collective defacing of all the noise regions then we get and the final state would take this form here and when we have our frequent equals beta so when we have our plus states then the diskette calls squared fetuses this is the worst possible scenario and in the best possible scenario where we have alpha is 1 all betas 1 so and 0 and 1 states we get perfect fidelity every single time and we're going to move on to our results now and so this is our 1st results is on how the number of wave plates facts are resultant fidelity as we can see as we increase number way play surprisingly the Fidelity's of course if we take into account areas within the wave place them would X expect this to level off and possibly go down the and on the top here we've got 5 of land 10 kilometers and noise region of 10 meters the standard deviation or noise read the variation north regions 3 meters and we can see incomparably of the point that to achieve 19 8 cent fidelity we need 610 wave plates which would involve replacing them roughly 8 comma decimal 2 meters apart so that ballistic distance apart in place now way plates is something we can actually considered during would be using passive way plates with model that so far as X. pulses but obviously there Vantu's using a mixture of Expo some why posts we found out and yesterday and and
09:51
here we hold very take 500 way plates on fiber length of tutors and we can see and how much defacing we can correct for we think we got this region here where we can correct for 98 and we can correct up to 98 cents so we begin to think about using a suite of quant communication we probably need to get some further improvements and we got this region here where we got about 89 % which should be suitable for the for so hopefully from reasonable model enough fiber we should be able to use and wait plates and dynamic of the coupling to correct for the phasing and
10:29
that we talk I'm afraid to say to them what we shared now results is there we knew the CPNT sequence of dynamical to coupling to correct for defacing an optical fibers when we got noise region of 10 meters and standard deviation this of 3 meters and standard deviation of fringes of 100 gradients for 10 kilometer fiber 610 way plays required to achieve a fidelity 98 cents and we're gonna go on what happens if we introduce errors and these wavelengths flights thank you very much for the class the the thank you that was crystal clear and are there any questions just a clarification on the technology side what you mean when you say you put wait played enough either so that's something we've got or we propose several proposals in our paper or on how to do that but it's not in necessarily be easy I think there's some suggestions of using twists and other things that have to get back to you on the details could you give us some further details on how you model the noise on the fiber and so what happens in each section of noise in each section of noise we
12:00
generated rat value for delta N. between with the standard deviations
12:06
given by the ones on the graph
12:09
and with the mean of 0 and
12:16
we have dealt and lasting for freelance that so so the noises is basically a fluctuation in the length of the fiber and the
12:26
noise is caused by fluctuations in the buyer for India and along the length of the
12:33
fiber coming back to the technology side as he
12:45
talked about only using passive with plates but there could be electrooptic modulators instead of face plates and the system very amenable to boards what dynamic feedback into work out the optimal dynamical the coupling based on the mean of the phase responsible polar like going through that fiber morning if the service future directions and I think it's a good idea it's not something that had a chance let can yet I think it's something we want to move on to the context is 2nd thing of papers on work crime any more questions alright if not then thanks again and we we have a 20 minute of it that was the