Friday, July 5, 2013

1307.1136 (Joseph M. Renes et al.)

Efficient Quantum Polar Codes Requiring No Preshared Entanglement    [PDF]

Joseph M. Renes, David Sutter, Frédéric Dupuis, Renato Renner
We construct an explicit entanglement distillation scheme which achieves a communication rate not less than the coherent information when used to transmit quantum information over a noisy quantum channel. For Pauli and erasure channels we also present efficient encoding and decoding algorithms for this communication scheme based on polar codes, but which do not require the sender and receiver to share any entanglement before the protocol begins. Due to the existence of degeneracies in the involved error-correcting codes it is indeed possible that the rate of the scheme exceeds the coherent information. We provide a simple criterion which indicates such performance. Finally we discuss how the scheme can be used for secret key distillation as well as private channel coding.
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