# Upper bounds for the Holevo quantity and their use

## TL;DR

This paper introduces new, easily computable upper bounds for the Holevo quantity in quantum information, which improve existing estimates and are applicable to both finite and infinite-dimensional quantum channels.

## Contribution

It proposes a family of tight upper bounds for the Holevo quantity based on probabilistic and metric ensemble characteristics, applicable to various quantum systems.

## Key findings

- Upper bounds depend on a reference state and ensemble metrics.
- Bounds are tight for large energy in multi-mode oscillators.
- Results improve estimates for quantum channel capacities.

## Abstract

We present a family of easily computable upper bounds for the Holevo quantity of ensemble of quantum states depending on a reference state as a free parameter. These upper bounds are obtained by combining probabilistic and metric characteristics of the ensemble. We show that appropriate choice of the reference state gives tight upper bounds for the Holevo quantity which in many cases improve existing estimates in the literature. We also present upper bound for the Holevo quantity of a generalized ensemble of quantum states with finite average energy depending on metric divergence of the ensemble. The specification of this upper bound for the multi-mode quantum oscillator is tight for large energy. The above results are used to obtain tight upper bounds for the Holevo capacity of finite-dimensional and infinite-dimensional energy-constrained quantum channels depending on metric characteristics of the channel output.