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arXiv · 1210.4722

Finite blocklength converse bounds for quantum channels

William Matthews·Stephanie Wehner
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Abstract

We derive upper bounds on the rate of transmission of classical information over quantum channels by block codes with a given blocklength and error probability, for both entanglement-assisted and unassisted codes, in terms of a unifying framework of quantum hypothesis testing with restricted measurements. Our bounds do not depend on any special property of the channel (such as memorylessness) and generalise both a classical converse of Polyanskiy, Poor, and Verdú as well as a quantum converse of Renner and Wang, and have a number of desirable properties. In particular our bound on entanglement-assisted codes is a semidefinite program and for memoryless channels its large blocklength limit is the well known formula for entanglement-assisted capacity due to Bennett, Shor, Smolin and Thapliyal.

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William Matthews, Stephanie Wehner. 2014-06-27. Finite blocklength converse bounds for quantum channels. https://doi.org/10.1109/tit.2014.2353614

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