Linear Quantum Error Correction

Abstract

We develop a generalized theory of quantum error correction (QEC) that applies to any linear map, in particular maps that are not completely positive (CP). This theory describes entanglement-assisted QEC for invertible noise maps, which we use to provides an example of the physical implementation of non-CP recovery maps. We argue that a consistent map-based theory of fault-tolerant QEC (whether Markovian or not) requires linear, non-CP maps, and that this impacts the value of the fault-tolerance threshold.

This paper has been withdrawn as it has been superseded by arXiv:0902.2478

Cited by in corpus (2)

• Computing Stabilized Norms for Quantum Operations via the Theory of Completely Bounded Maps
• Topics in quantum information and the theory of open quantum systems