A Holevo-Type Bound for a Hilbert Schmidt Distance Measure


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 by using a quantum channel while Bob is performing some projective measurements. 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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Tamir, B. and Cohen, E. (2015) A Holevo-Type Bound for a Hilbert Schmidt Distance Measure. Journal of Quantum Information Science, 5, 127-133. doi: 10.4236/jqis.2015.54015.

Conflicts of Interest

The authors declare no conflicts of interest.


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