title: 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. 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 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.
authors.affiliation: Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543 Singapore.
authors.forename: Cédric
authors.initials: C
authors.lastname: Bény
authors.forename: Ognyan
authors.initials: O
authors.lastname: Oreshkov