arXiv:1105.3321 · IEEE Transactions on Information Theory

One-Shot Entanglement-Assisted Quantum and Classical Communication

Nilanjana Datta, Min-Hsiu Hsieh

Published Nov 21, 2012• 52 citations

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 analog 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.

DOI: 10.1109/tit.2012.2228737

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