English

Linear Quantum Error Correction

Quantum Physics 2009-10-21 v2

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.

Keywords

Cite

@article{arxiv.0708.1953,
  title  = {Linear Quantum Error Correction},
  author = {A. Shabani and D. A. Lidar},
  journal= {arXiv preprint arXiv:0708.1953},
  year   = {2009}
}

Comments

This paper has been withdrawn as it has been superseded by arXiv:0902.2478

R2 v1 2026-06-21T09:07:29.961Z