Universal bounds for the Holevo quantity, coherent information \\ and the Jensen-Shannon divergence

Abstract

The Holevo quantity provides an upper bound for the mutual information between the sender of a classical message encoded in quantum carriers and the receiver. Applying the strong sub-additivity of entropy we prove that the Holevo quantity associated with an initial state and a given quantum operation represented in its Kraus form is not larger than the exchange entropy. This implies upper bounds for the coherent information and for the quantum Jensen--Shannon divergence. Restricting our attention to classical information we bound the transmission distance between any two probability distributions by the entropic distance, which is a concave function of the Hellinger distance.

5 pages, 2 figures

References in corpus (3)

• Properties of Classical and Quantum Jensen-Shannon Divergence
• On the metric character of the quantum Jensen-Shannon divergence
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