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Entanglement Theory Quantum Correlations

Simplifying additivity problems using direct sum constructions

arXiv
Authors: Motohisa Fukuda, Michael M. Wolf

Year

2007

Paper ID

50625

Status

Preprint

Abstract Read

~2 min

Abstract Words

107

Citations

N/A

Abstract

We study the additivity problems for the classical capacity of quantum channels, the minimal output entropy and its convex closure. We show for each of them that additivity for arbitrary pairs of channels holds iff it holds for arbitrary equal pairs, which in turn can be taken to be unital. In a similar sense, weak additivity is shown to imply strong additivity for any convex entanglement monotone. The implications are obtained by considering direct sums of channels (or states) for which we show how to obtain several information theoretic quantities from their values on the summands. This provides a simple and general tool for lifting additivity results.

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  • This paper contributes to the Entanglement Theory & Quantum Correlations research area in the Quantum Articles archive.
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  • We study the additivity problems for the classical capacity of quantum channels, the minimal output entropy and its convex closure.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:0704.1092 [2] arXiv https://arxiv.org/abs/0704.1092 [3] Publisher https://arxiv.org/abs/0704.1092

Local Citation Graph (Related-Paper Links)

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External citation index: OpenAlex citation signal

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