2009/07/31 by Cédric Bény, Ognyan Oreshkov · 1 citation
Physics and Astronomy · #quant-ph
paper · pdf · doi:10.1103/physrevlett.104.120501
published as Phys. Rev. Lett. 104, 120501 (2010) · minor clarifications, typos edited, references added.
arxiv created 2010/03/24 · arxiv updated 2010/03/25
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.