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MiS Preprint
20/2013
Universal upper bound for the Holevo information induced by a quantum operation
Lin Zhang, Junde Wu and Shao-Ming Fei
Abstract
Let $\mathcal{H}_A\otimes \mathcal{H}_B$ be a bipartite system and $\rho_{AB}$ a quantumstate on $\mathcal{H}_A\otimes \mathcal{H}_B$, $\rho_A = Tr_B (\rho_{AB})$, $\rho_B =Tr_A (\rho_{AB})$. Then each quantum operation $\Phi_B$ on quantum system $\mathcal{H}_B$ can induce a quantum ensemble $\set{(p_\mu,\rho_{A,\mu})}$ on quantum system $\mathcal{H}_A$. In this paper, we show that the Holevo quantity $\mathcal{H}i\set{(p_\mu,\rho_{A,\mu})}$ of the quantum ensemble $\set{(p_\mu,\rho_{A,\mu})}$ can be upper bounded by $\mathrm{S}(\rho_B)$. By using the result, we answer partly a conjecture of Fannes, de Melo, Roga and Życzkowski.
