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This paper has been withdrawn as it has been superseded by arXiv:0902.2478