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.