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arXiv · 1110.5979

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

Lin Zhang·Junde Wu·Shao-Ming Fei
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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.

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Lin Zhang, Junde Wu, Shao-Ming Fei. 2011-10-27. Universal upper bound for the Holevo information induced by a quantum operation. https://doi.org/10.1016/j.physleta.2012.10.014

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