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arXiv · 1003.5765

The entropy gain of infinite-dimensional quantum channels

A. S. Holevo
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Abstract

In the present paper we study the entropy gain $H(\Phi [\rho])-H(\rho)$ for infinite-dimensional channels $\Phi$. We show that unlike finite-dimensional case where the minimal entropy gain is always nonpositive \cite{al}, there is a plenty of channels with positive minimal entropy gain. We obtain the new lower bound and compute the minimal entropy gain for a broad class of Bosonic Gaussian channels by proving that the infimum is attained on the Gaussian states.

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A. S. Holevo. 2010-03-30. The entropy gain of infinite-dimensional quantum channels. https://doi.org/10.1134/s1064562410050133

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