Upper bounds on the Holevo quantity arising from the fundamental entropic inequality

TL;DR

This paper derives tight upper bounds on the Holevo quantity for quantum state ensembles using a fundamental entropic inequality, enhancing understanding of quantum information limits.

Contribution

It introduces a new relation for the Holevo quantity based on an entropic inequality, applicable to both discrete and continuous quantum ensembles.

Findings

Provides tight upper bounds on the Holevo quantity

Relates the Holevo quantity to auxiliary ensembles' quantities

Offers accurate bounds using probabilities and metric characteristics

Abstract

We show how the fundamental entropic inequality proved recently in [arXiv:2408.15306] can be applied to obtain a useful relation for the Holevo quantity of discrete and continuous ensembles of quantum states. This relation gives a tight upper bound on the Holevo quantity of a given ensemble $\mu$ expressed in terms of the Holevo quantities of two auxiliary ensembles $\mu_+$ and $\mu_-$ produced by $\mu$. Among others, this implies quite accurate upper bounds on the Holevo quantity of a discrete ensemble of quantum states expressed via the probabilities and the metric characteristics of an ensemble.