One-shot entanglement-assisted quantum and classical communication
Abstract
We study entanglement-assisted quantum and classical communication over a single use of a quantum channel, which itself can correspond to a finite number of uses of a channel with arbitrarily correlated noise. We obtain characterizations of the corresponding one-shot capacities by establishing upper and lower bounds on them in terms of the difference of two smoothed entropic quantities. In the case of a memoryless channel, the upper and lower bounds converge to the known single-letter formulas for the corresponding capacities, in the limit of asymptotically many uses of it. Our results imply that the difference of two smoothed entropic quantities characterizing the one-shot entanglement-assisted capacities serves as a one-shot analogue of the mutual information, since it reduces to the mutual information, between the output of the channel and a system purifying its input, in the asymptotic, memoryless scenario.
Cite
@article{arxiv.1105.3321,
title = {One-shot entanglement-assisted quantum and classical communication},
author = {Nilanjana Datta and Min-Hsiu Hsieh},
journal= {arXiv preprint arXiv:1105.3321},
year = {2013}
}
Comments
10 pages, 2 figures. Title changed due to new results on the one-shot entanglement-assisted quantum communication. In addition, an error in the previous version regarding the converse proof of the one-shot EAC capacity has been corrected