The entropy gain of infinite-dimensional quantum channels

In the present paper we study the entropy gain $H(Φ[ρ])-H(ρ)$ for infinite-dimensional channels $Φ$. 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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