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Quantum polar codes for arbitrary channels · Around

2012

Quantum polar codes for arbitrary channels

Wilde, Mark M., Renes, Joseph M.

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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 channel.

We first demonstrate the coding scheme for arbitrary quantum channels with qubit inputs, and we show that quantum data can be reliably decoded by O(N) rounds of coherent quantum successive cancellation, followed by N controlled-NOT gates (where N is the number of channel uses).
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.

Built on

T. A. Brun, I. Devetak, and M.-H. Hsieh, “Correcting quantum errors with entanglement,” Science , vol. 314, pp. 436–439, Oct. 2006
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J. M. Renes and J.-C. Boileau, “Physical underpinnings of privacy,” Physical Review A , vol. 78, p. 032335, September 2008
2008
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G. Smith and J. Yard, “Quantum communication with zero-capacity channels,” Science , vol. 321, pp. 1812–1815, September 2008
2008
Earlier work this paper cites.
E. Arikan, “Channel polarization: A method for constructing capacity-achieving codes for symmetric binary-input memoryless channels,” IEEE Trans. Inf. Theory , vol. 55, no. 7, pp. 3051–3073, July 2009
2009
Earlier work this paper cites.

Similar

——, “Conjectured strong complementary information tradeoff,” Phys. Rev. Lett. , vol. 103, p. 020402, July 2009
2009
Cited alongside, same era.
J.-C. Boileau and J. M. Renes, “Optimal state merging without decoupling,” in Theory of Quantum Comp., Comm., and Crypt. , ser. Lecture Notes in Computer Science, vol. 5906, 2009, pp. 76–84
2009
Cited alongside, same era.
E. Sasoglu, E. Telatar, and E. Arikan, “Polarization for arbitrary discrete memoryless channels,” 2009 IEEE Information Theory Workshop , pp. 144–148, 2009, arXiv:0908.0302
Original
2009
Cited alongside, same era.
J. M. Renes, “Approximate quantum error correction via complementary observables,” March 2010, arXiv:1003.1150
Original
2010
Cited alongside, same era.

Then

——, “Duality of privacy amplification against quantum adversaries and data compression with quantum side information,” Proceedings of the Royal Society A , vol. 467, no. 2130, pp. 1604–1623, 2011
2011
Later among the works it cites.
J. M. Renes, F. Dupuis, and R. Renner, “Efficient quantum polar coding,” September 2011, arXiv:1109.3195
Original
2011
Later among the works it cites.
M. M. Wilde and S. Guha, “Polar codes for degradable quantum channels,” September 2011, arXiv:1109.5346
Original
2011
Later among the works it cites.
M. M. Wilde and S. Guha, “Polar codes for classical-quantum channels,” September 2011, arXiv:1109.2591
Original
2011
Later among the works it cites.

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