General conditions for approximate quantum error correction and near-optimal recovery channels

Details General conditions for approximate quantum error correction and near-optimal recovery channels General conditions for approximate quantum error correction and near-optimal recovery channels

2009-07-30

arxiv.org/abs/0907.5391v4

Phys. Rev. Lett. 104, 120501 (2010)

Physics

Quantum Physics

minor clarifications, typos edited, references added.

Scientific paper

10.1103/PhysRevLett.104.120501

We derive necessary and sufficient conditions for the approximate correctability of a quantum code, generalizing the Knill-Laflamme conditions for exact error correction. Our measure of success of the recovery operation is the worst-case entanglement fidelity of the overall process. We show that the optimal recovery fidelity can be predicted exactly from a dual optimization problem on the environment causing the noise. We use this result to obtain an easy-to-calculate estimate of the optimal recovery fidelity as well as a way of constructing a class of near-optimal recovery channels that work within twice the minimal error. In addition to standard subspace codes, our results hold for subsystem codes and hybrid quantum-classical codes.

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