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The entropy gain of infinite-dimensional quantum channels
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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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Cited by 1 Pith paper
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Information geometry of bosonic Gaussian thermal states
Exact integral formulas are derived for the information matrices, derivatives, and symmetric logarithmic derivatives of bosonic Gaussian thermal states.
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