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

M. E. Shirokov

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arXiv · 2506.05335

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

M. E. Shirokov

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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.

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M. E. Shirokov. 2025-06-05. Upper bounds on the Holevo quantity arising from the fundamental entropic inequality. https://arxiv.org/abs/2506.05335

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