A Holevo-type bound for a Hilbert Schmidt distance measure
arXiv:1502.04691 · doi:10.4236/jqis.2015.54015
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.
8 pages. Accepted to Journal of Quantum Information Science
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- New Logical Foundations for Quantum Information Theory: Introduction to Quantum Logical Information Theory
- On Classical and Quantum Logical Entropy: The analysis of measurement
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- Computing partial transposes and related entanglement functions