The entropy gain of infinite-dimensional quantum channels

TL;DR

This paper investigates the entropy gain in infinite-dimensional quantum channels, revealing that unlike finite-dimensional channels, many have positive minimal entropy gain, especially for Bosonic Gaussian channels.

Contribution

It introduces a new lower bound for entropy gain and shows that the infimum is attained on Gaussian states for a broad class of Bosonic Gaussian channels.

Findings

Many infinite-dimensional channels have positive minimal entropy gain.

The minimal entropy gain is attained on Gaussian states for Bosonic Gaussian channels.

A new lower bound for entropy gain is established.

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.