A Holevo-Type Bound for a Hilbert Schmidt Distance Measure

Boaz Tamir; Eliahu Cohen

doi:10.4236/jqis.2015.54015

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Journal of Quantum Information Science > Vol.5 No.4, December 2015

A Holevo-Type Bound for a Hilbert Schmidt Distance Measure ()

¹Faculty of Interdisciplinary Studies, Bar-Ilan University, Ramat-Gan, Israel.
²H.H. Wills Physics Laboratory, University of Bristol, Bristol, UK.
³School of Physics and Astronomy, Tel-Aviv University, Tel-Aviv, Israel.

DOI: 10.4236/jqis.2015.54015 PDF HTML XML 3,654 Downloads 4,144 Views Citations

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 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.

Keywords

Holevo Bound, Hilbert-Schmidt Norm, Entanglement Measures

Share and Cite:

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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