Private Quantum Coding for Quantum Relay Networks

The relay encoder is an unreliable probabilistic device which is aimed at helping the communication between the sender and the receiver. In this work we show that in the quantum setting the probabilistic behavior can be completely eliminated. 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.

[1]  Joseph M. Renes,et al.  Efficient Quantum Polar Coding , 2011, ArXiv.

[2]  Sandor Imre,et al.  Informational geometric analysis of superactivation of asymptotic quantum capacity of zero-capacity optical quantum channels , 2011, OPTO.

[3]  Refractor.  Uncertainty , 2001, The Lancet.

[4]  Sandor Imre,et al.  Quantum Polar Coding for Noisy Optical Quantum Channels , 2012 .

[5]  Igor Devetak.  The private classical capacity and quantum capacity of a quantum channel , 2005, IEEE Transactions on Information Theory.

[6]  Erdal Arikan,et al.  Channel Polarization: A Method for Constructing Capacity-Achieving Codes for Symmetric Binary-Input Memoryless Channels , 2008, IEEE Transactions on Information Theory.

[7]  Joseph M. Renes,et al.  Optimal State Merging without Decoupling , 2009, TCQ.

[8]  Jonathan Oppenheim,et al.  Public Quantum Communication and Superactivation , 2010, IEEE Transactions on Information Theory.

[9]  Laszlo Gyongyosi,et al.  Algorithmic superactivation of asymptotic quantum capacity of zero-capacity quantum channels , 2012, Inf. Sci..

[10]  Dominic C. O'Brien,et al.  Wireless Myths, Realities, and Futures: From 3G/4G to Optical and Quantum Wireless , 2012, Proceedings of the IEEE.

[11]  Abbas El Gamal,et al.  Capacity theorems for the relay channel , 1979, IEEE Trans. Inf. Theory.

[12]  Graeme Smith,et al.  Quantum Communication with Zero-Capacity Channels , 2008, Science.

[13]  Sandor Imre,et al.  Quantum Computing and Communications: An Engineering Approach , 2005 .

[14]  Saikat Guha,et al.  Polar Codes for Classical-Quantum Channels , 2011, IEEE Transactions on Information Theory.

[15]  Joseph M. Renes,et al.  Quantum polar codes for arbitrary channels , 2012, 2012 IEEE International Symposium on Information Theory Proceedings.

[16]  Matthias Christandl,et al.  Uncertainty, monogamy, and locking of quantum correlations , 2005, IEEE Transactions on Information Theory.

[18]  Joseph M Renes,et al.  Efficient polar coding of quantum information. , 2011, Physical review letters.

[19]  Alexander Vardy,et al.  Achieving the Secrecy Capacity of Wiretap Channels Using Polar Codes , 2010, IEEE Transactions on Information Theory.

[20]  Dave Touchette,et al.  Trade-off capacities of the quantum Hadamard channels , 2010, ArXiv.

[21]  Joseph M. Renes,et al.  Polar codes for private classical communication , 2012, 2012 International Symposium on Information Theory and its Applications.

[22]  Mikael Skoglund,et al.  Nested Polar Codes for Wiretap and Relay Channels , 2010, IEEE Communications Letters.

[23]  Fernando G S L Brandão,et al.  When does noise increase the quantum capacity? , 2012, Physical review letters.

[24]  Sandor Imre,et al.  Advanced Quantum Communications: An Engineering Approach , 2012 .