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Paulsen, V. (2002) Completely Bounded Maps and Operator Algebras. Cambridge University Press, Cambridge, UK.

has been cited by the following article:

• TITLE: A Holevo-Type Bound for a Hilbert Schmidt Distance Measure

  AUTHORS: Boaz Tamir, Eliahu Cohen

  KEYWORDS: Holevo Bound, Hilbert-Schmidt Norm, Entanglement Measures

  JOURNAL NAME: Journal of Quantum Information Science, Vol.5 No.4, December 17, 2015

  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.