Universal upper bound for the Holevo information induced by a quantum operation

TL;DR

This paper establishes a universal upper bound for the Holevo information generated by quantum operations, relating it to subsystem entropies, and addresses a conjecture in quantum information theory.

Contribution

It provides a new upper bound for the Holevo quantity induced by quantum operations, advancing understanding of quantum information limits.

Findings

Holevo quantity is bounded by subsystem entropies.

The result partially confirms a conjecture by Fannes et al.

Provides a theoretical limit on information transfer in quantum systems.

Abstract

Let $\cH_A\ot \cH_B$ be a bipartite system and $\rho_{AB}$ a quantum state on $\cH_A\ot \cH_B$, $\rho_A = \Ptr{B}{\rho_{AB}}$, $\rho_B = \Ptr{A}{\rho_{AB}}$. Then each quantum operation $\Phi_B$ on the quantum system $\cH_B$ can induce a quantum ensemble $\set{(p_\mu,\rho_{A,\mu})}$ on quantum system $\cH_A$. In this paper, we show that the Holevo quantity $\chi\set{(p_\mu,\rho_{A,\mu})}$ of the quantum ensemble $\set{(p_\mu,\rho_{A,\mu})}$ can be upper bounded by both subsystem entropies. By using the result, we answer partly a conjecture of Fannes, de Melo, Roga and \.{Z}yczkowski.