General conditions for approximate quantum error correction and near-optimal recovery channels
Abstract
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.
Keywords
Cite
@article{arxiv.0907.5391,
title = {General conditions for approximate quantum error correction and near-optimal recovery channels},
author = {Cédric Bény and Ognyan Oreshkov},
journal= {arXiv preprint arXiv:0907.5391},
year = {2010}
}
Comments
minor clarifications, typos edited, references added.