Approximate quantum error correction, random codes, and quantum channel capacity

Details Approximate quantum error correction, random codes, and quantum channel capacity Approximate quantum error correction, random codes, and quantum channel capacity

2007-01-15

arxiv.org/abs/quant-ph/0701102v2

Phys. Rev. A 75, 062315 (2007)

Physics

Quantum Physics

29 pages, final version to appear in Phys. Rev. A, improved lower bound for code entanglement fidelity, simplified proof

Scientific paper

10.1103/PhysRevA.75.062315

We work out a theory of approximate quantum error correction that allows us to derive a general lower bound for the entanglement fidelity of a quantum code. The lower bound is given in terms of Kraus operators of the quantum noise. This result is then used to analyze the average error correcting performance of codes that are randomly drawn from unitarily invariant code ensembles. Our results confirm that random codes of sufficiently large block size are highly suitable for quantum error correction. Moreover, employing a lemma of Bennett, Shor, Smolin, and Thapliyal, we prove that random coding attains information rates of the regularized coherent information.

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