title: Perturbative quantum error correction.
abstract: We derive simple necessary and sufficient conditions under which a quantum channel obtained from an arbitrary perturbation from the identity can be reversed on a given code to the lowest order in fidelity. We find the usual Knill-Laflamme conditions applied to a certain operator subspace which, for a generic perturbation, is generated by the Lindblad operators. For a weak interaction with an environment, the error space to be corrected is a subspace of that spanned by the interaction operators, selected by the environment's initial state.
authors.affiliation: Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543.
authors.forename: Cédric
authors.initials: C
authors.lastname: Bény