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arXiv · 1502.04691

A Holevo-type bound for a Hilbert Schmidt distance measure

Boaz Tamir·Eliahu Cohen
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Abstract

We prove a new version of the Holevo bound employing the Hilbert-Schmidt norm instead of the Kullback-Leibler divergence. Suppose Alice is sending classical information to Bob using a quantum channel, while Bob is performing some projective measurement. We bound the classical mutual information in terms of the Hilbert-Schmidt norm by its quantum Hilbert-Schmidt counterpart. This constitutes a Holevo-type upper bound on the classical information transmission rate via a quantum channel. The resulting inequality is rather natural and intuitive relating classical and quantum expressions using the same measure.

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Boaz Tamir, Eliahu Cohen. 2015-10-12. A Holevo-type bound for a Hilbert Schmidt distance measure. https://doi.org/10.4236/jqis.2015.54015

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