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

Let HA⊗HBHA⊗HB be a bipartite system and ρABρAB a quantum state on HA⊗HBHA⊗HB, ρA=TrB(ρAB)ρA=TrB(ρAB), ρB=TrA(ρAB)ρB=TrA(ρAB). Then each quantum operation ΦBΦB on the quantum system HBHB can induce a quantum ensemble {(pμ,ρA,μ)}{(pμ,ρA,μ)} on quantum system HAHA. In this Letter, we show that the Holevo quantity χ{(pμ,ρA,μ)}χ{(pμ,ρA,μ)} of the quantum ensemble {(pμ,ρA,μ)}{(pμ,ρA,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.

► A universal upper bound of quantum ensemble is obtained. ► Using the result, a conjecture is answered partly. ► A characterization of positivity of an operator matrix is discussed.