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Polar Codes for Degradable Quantum Channels

Mark M. Wilde, Saikat Guha
2013 IEEE Transactions on Information Theory  
In the current paper, we build on their work and demonstrate how to construct quantum wiretap polar codes that achieve the symmetric private capacity of a degraded quantum wiretap channel with a classical  ...  Due to the Schumacher-Westmoreland correspondence between quantum privacy and quantum coherence, we can construct quantum polar codes by operating these quantum wiretap polar codes in superposition, much  ...  Polar codes for degradable quantum channels Mark M.  ... 
doi:10.1109/tit.2013.2250575 fatcat:cppyw6jm2za6zn4puvwx6se674

Quantum Information Transmission Over a Partially Degradable Channel

Laszlo Gyongyosi
2014 IEEE Access  
We investigate a quantum coding for quantum communication over a PD (partially degradable) degradable quantum channel.  ...  We define a coding scheme for PD-channels and give the achievable rates of quantum communication.  ...  Polar code sets for a PD channel.  ... 
doi:10.1109/access.2014.2308574 fatcat:oz7g43uyejendmmkitfvwiqkdi

Polaractivation of hidden private classical capacity region of quantum channels

Laszlo Gyongyosi
2013 2013 IEEE Symposium on Swarm Intelligence (SIS)  
We define a new phenomenon for communication over noisy quantum channels. The investigated solution is called polaractivation and based on quantum polar encoding.  ...  Polaractivation is a natural consequence of the channel polarization effect in quantum systems and makes possible to open the hidden capacity regions of a noisy quantum channel by using the idea of rate  ...  We show that the quantum polar coding can be used for the polaractivation of hidden capacity regions of a noisy quantum channel [26] [27] [28] , [42] .  ... 
doi:10.1109/sis.2013.6615170 dblp:conf/swis/Gyongyosi13 fatcat:zh7g55mrjbbvrix6vhpyiuzzi4

Private Quantum Coding for Quantum Relay Networks [article]

Laszlo Gyongyosi, Sandor Imre
2013 arXiv   pre-print
We also show how to combine quantum polar encoding with superactivation-assistance in order to achieve reliable and capacity-achieving private communication over noisy quantum relay channels.  ...  In this work we show that in the quantum setting the probabilistic behavior can be completely eliminated.  ...  [2] , using their nested polar relay channel codes.  ... 
arXiv:1208.0661v2 fatcat:zzdbd2yulvfetd2hj3w4gddhm4

Multiletter codes to boost superadditivity of coherent information in quantum communication lines with polarization dependent losses [article]

Sergey N. Filippov
2021 arXiv   pre-print
However, even for simple physical models of channels it is rather difficult to detect the superadditivity and find the advantageous multiletter codes.  ...  We show that in the asymptotic limit of the infinite code length the superadditivity phenomenon takes place whenever the communication channel is neither degradable nor antidegradable.  ...  FIG. 1 : 1 FIG. 1: Attenuation factors pH and pV for horizontally and vertically polarized photons for which the quantum channel (3) is degradable (red area), antidegradable (green area), both degradable  ... 
arXiv:2109.03577v1 fatcat:usftmjur4bfrlez3t2n4whwmjq

Private Quantum Coding for Quantum Relay Networks [chapter]

Laszlo Gyongyosi, Sándor Imre
2012 Lecture Notes in Computer Science  
We also show how to combine quantum polar encoding with superactivation-assistance in order to achieve private communication over noisy quantum relay channels.  ...  In this work we show that in the quantum setting the probabilistic behavior can be completely eliminated.  ...  [2] , using their nested polar relay channel codes.  ... 
doi:10.1007/978-3-642-32808-4_22 fatcat:qjmfudw6r5hztfzobtronyhqsi

Quantum polar codes for arbitrary channels

Mark M. Wilde, Joseph M. Renes
2012 2012 IEEE International Symposium on Information Theory Proceedings  
We also find that the entanglement consumption rate of the code vanishes for degradable quantum channels. Finally, we extend the coding scheme to channels with multiple qubit inputs.  ...  We construct a new entanglement-assisted quantum polar coding scheme which achieves the symmetric coherent information rate by synthesizing "amplitude" and "phase" channels from a given, arbitrary quantum  ...  ZERO E-BIT RATE FOR DEGRADABLE CHANNELS We can now prove that the entanglement consumption rate of our quantum polar coding scheme vanishes for an arbitrary degradable quantum channel.  ... 
doi:10.1109/isit.2012.6284203 dblp:conf/isit/WildeR12 fatcat:6kitxxzvfjcuppwbh5zpzu7un4

Magic state distillation with punctured polar codes [article]

Anirudh Krishna, Jean-Pierre Tillich
2019 arXiv   pre-print
We present a scheme for magic state distillation using punctured polar codes. Our results build on some recent work by Bardet et al.  ...  (ISIT, 2016) who discovered that polar codes can be described algebraically as decreasing monomial codes.  ...  We would also like to thank Colin Trout for detailed feedback on an earlier draft of this work, and Pavithran Iyer and Maxime Tremblay for many helpful comments.  ... 
arXiv:1811.03112v2 fatcat:t2ds663j55a2ja7opjj6mdlbzq

Polar codes for private classical communication [article]

Mark M. Wilde, Joseph M. Renes
2012 arXiv   pre-print
We construct a new secret-key assisted polar coding scheme for private classical communication over a quantum or classical wiretap channel.  ...  We find that the secret-key consumption rate of the scheme vanishes for an arbitrary degradable quantum wiretap channel.  ...  for an arbitrary degradable quantum wiretap channel  ... 
arXiv:1203.5794v1 fatcat:rysi2agwnrbfnobad3xebmgxme

Polar Codes for Private and Quantum Communication Over Arbitrary Channels

Joseph M. Renes, Mark M. Wilde
2014 IEEE Transactions on Information Theory  
We construct new polar coding schemes for the transmission of quantum or private classical information over arbitrary quantum channels.  ...  Both schemes are built from a polar coding construction capable of transmitting classical information over a quantum channel [Wilde and Guha, IEEE Transactions on Information Theory, in press].  ...  Thus, this same argument implies that the entanglement consumption rate for the quantum polar codes in [8] vanishes for general degradable quantum channels because the rate of the phase-good channels  ... 
doi:10.1109/tit.2014.2314463 fatcat:q6pwzkoxlng2zm5sbjwwf2jwoq

Polar codes in quantum information theory [article]

Christoph Hirche
2015 arXiv   pre-print
We also discuss polar codes for quantum communication over quantum channels and state results towards codes for compound quantum channels in this setting.  ...  In addition we use polar codes to prove a new achievable rate region for the classical-quantum broadcast channel.  ...  Universal polar codes for degraded channels in the simultaneous scheme We call a channel N 1 degraded with respect to another channel N 2 , denoted by N 1 N 2 , if there exists a degrading channel D such  ... 
arXiv:1501.03737v1 fatcat:ngwdymwwp5a7bgupameafktd3e

Universal polar codes for more capable and less noisy channels and sources

David Sutter, Joseph M. Renes
2014 2014 IEEE International Symposium on Information Theory  
We prove two results on the universality of polar codes for source coding and channel communication.  ...  This result extends to channel coding for discrete memoryless channels.  ...  Every polar code built for V can be used for W with SC decoding Polar codes are universal for less noisy channels Theorem: universality for less noisy channels Let W ∶ X → Y and V ∶ X → Z be two DMCs such  ... 
doi:10.1109/isit.2014.6875075 dblp:conf/isit/SutterR14 fatcat:b2gaxwjjajfhzcomyutjxp2wfy

The Structure and Quantum Capacity of a Partially Degradable Quantum Channel

Laszlo Gyongyosi
2014 IEEE Access  
On the other hand, there is no general rule for the behavior of quantum capacity for non-degradable quantum channels.  ...  We introduce the set of partially degradable (PD) quantum channels to answer the question of additivity of quantum capacity for a well-separable subset of non-degradable channels.  ...  The code structure of the polar code for quantum communication over a degradable PD channel. Set will be used for quantum communication.  ... 
doi:10.1109/access.2014.2317652 fatcat:6yedrc6byvh25fgnfo6octjrri

Alignment of Polarized Sets

Joseph M. Renes, David Sutter, S. Hamed Hassani
2016 IEEE Journal on Selected Areas in Communications  
Finally we show that these conditions imply that the simple quantum polar coding scheme of Renes et al. [Phys. Rev.  ...  Understanding the alignment of the polarized sets is important as it is directly related to universality properties of the induced polar codes, which are essential in particular for network coding problems  ...  ENTANGLEMENT ASSISTANCE FOR QUANTUM POLAR CODES Recently, the polarization phenomenon has been used to construct efficient codes, quantum polar codes, for transmitting quantum information.  ... 
doi:10.1109/jsac.2015.2504271 fatcat:l3dy3cn6dvc5fiffkdngov4osq

Alignment of polarized sets

Joseph M. Renes, David Sutter, S. Hamed Hassani
2015 2015 IEEE International Symposium on Information Theory (ISIT)  
Finally we show that these conditions imply that the simple quantum polar coding scheme of Renes et al. [Phys. Rev.  ...  Understanding the alignment of the polarized sets is important as it is directly related to universality properties of the induced polar codes, which are essential in particular for network coding problems  ...  ENTANGLEMENT ASSISTANCE FOR QUANTUM POLAR CODES Recently, the polarization phenomenon has been used to construct efficient codes, quantum polar codes, for transmitting quantum information.  ... 
doi:10.1109/isit.2015.7282895 dblp:conf/isit/RenesSH15 fatcat:oeb7rvb2lzbtlhtiqgz5mcc4mq
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