Conditions for uniqueness of product representations for separable quantum channels and separable quantum states
Abstract
We give a sufficient condition that an operator sum representation of a separable quantum channel in terms of product operators is the unique product representation for that channel, and then provide examples of such channels for any number of parties. This result has implications for efforts to determine whether or not a given separable channel can be exactly implemented by local operations and classical communication. By the Choi-Jamiolkowski isomorphism, it also translates to a condition for the uniqueness of product state ensembles representing a given quantum state. These ideas follow from considerations concerning whether or not a subspace spanned by a given set of product operators contains at least one additional product operator.
Keywords
Cite
@article{arxiv.1210.0644,
title = {Conditions for uniqueness of product representations for separable quantum channels and separable quantum states},
author = {Scott M. Cohen},
journal= {arXiv preprint arXiv:1210.0644},
year = {2014}
}
Comments
Latest version has a new title, and is completely reorganized to emphasize the quantum information applications as opposed to the mathematical results. Version 3 has revised results for more than two parties, having discovered an error in earlier versions (see Conclusions for an explanation). Bipartite results are unchanged