The multiplicative domain in quantum error correction
Quantum Physics
2015-05-13 v1
Abstract
We show that the multiplicative domain of a completely positive map yields a new class of quantum error correcting codes. In the case of a unital quantum channel, these are precisely the codes that do not require a measurement as part of the recovery process, the so-called unitarily correctable codes. Whereas in the arbitrary, not necessarily unital case they form a proper subset of unitarily correctable codes that can be computed from properties of the channel. As part of the analysis we derive a representation theoretic characterization of subsystem codes. We also present a number of illustrative examples.
Cite
@article{arxiv.0811.0947,
title = {The multiplicative domain in quantum error correction},
author = {Man-Duen Choi and Nathaniel Johnston and David W. Kribs},
journal= {arXiv preprint arXiv:0811.0947},
year = {2015}
}
Comments
17 pages, preprint version