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

Abstract

Let $\cH_A\ot \cH_B$ be a bipartite system and $ρ_{AB}$ a quantum state on $\cH_A\ot \cH_B$, $ρ_A = \Ptr{B}{ρ_{AB}}$, $ρ_B = \Ptr{A}{ρ_{AB}}$. Then each quantum operation $Φ_B$ on the quantum system $\cH_B$ can induce a quantum ensemble $\set{(p_μ,ρ_{A,μ})}$ on quantum system $\cH_A$. In this paper, we show that the Holevo quantity $χ\set{(p_μ,ρ_{A,μ})}$ of the quantum ensemble $\set{(p_μ,ρ_{A,μ})}$ can be upper bounded by both subsystem entropies. By using the result, we answer partly a conjecture of Fannes, de Melo, Roga and Życzkowski.

9 pages, LaTeX, published version