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

TL;DR

This paper establishes universal bounds relating the Holevo quantity, coherent information, and Jensen-Shannon divergence, providing new insights into quantum information limits and classical probability distances.

Contribution

It proves that the Holevo quantity is bounded by exchange entropy and derives bounds for coherent information and Jensen-Shannon divergence using entropy properties.

Findings

Holevo quantity is bounded by exchange entropy

Upper bounds for coherent information are established

Entropic distance bounds classical probability distribution differences

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.