Quantum polar codes for arbitrary channels

Details Quantum polar codes for arbitrary channels Quantum polar codes for arbitrary channels

2012-01-13

arxiv.org/abs/1201.2906v1

Physics

Quantum Physics

9 pages, submission to the 2012 International Symposium on Information Theory (ISIT 2012), Boston, MA, USA

Scientific paper

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. This gives a near-explicit method for realizing one of the most striking phenomena in quantum information theory: the superactivation effect, whereby two quantum channels which individually have zero quantum capacity can have a non-zero quantum capacity when used together.

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