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

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