Upper Bounds for the Holevo Information Quantity and Their Use

2019/07/01 by M. E. Shirokov · 1 voice · 1 citation
Computer Science · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications

paper · doi:10.1134/s0032946019030013

openalex publication_date 2019/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We present a family of easily computable upper bounds for the Holevo (information) quantity of an 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 an appropriate choice of the reference state gives tight upper bounds for the Holevo quantity which in many cases improve the estimates existing in the literature. We also present an upper bound for the Holevo quantity of a generalized ensemble of quantum states with finite average energy depending on the metric divergence of an ensemble. In the case of a multi-mode quantum oscillator, this upper bound is tight for large energy. Upper bounds for the Holevo capacity of finite-dimensional quantum channels depending on metric characteristics of the channel output are obtained.

Citations

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Discussions

• You stumbled upon a real good one, OP! I would like to contribute a general comment and another partial answer. [I will however use standard notation: $S(\bullet)$ for von Neumann and $S(\bullet \Vert [stackexchange, 2 points]

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