A Holevo-Type Bound for a Hilbert Schmidt Distance Measure

Boaz Tamir, Eliahu Cohen

Research output: Contribution to journalArticle (Academic Journal)peer-review

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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.
Original languageEnglish
Pages (from-to)127-133
Number of pages7
JournalJournal of Quantum Information Science
Issue number4
Early online date17 Dec 2015
Publication statusPublished - Dec 2015


  • Holevo Bound
  • Hilbert-Schmidt Norm
  • Entanglement Measures


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