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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

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.

Received:
01.02.13
Published:
05.02.13
Keywords:
quantum state, Quantum operation, von Neumann entropy, Holevo quantity

Related publications

inJournal
2012 Repository Open Access
Lin Zhang, Junde Wu and Shao-Ming Fei

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

In: Physics Letters / A, 376 (2012) 47/48, pp. 3588-3592