Generalized minimal output entropy conjecture for one-mode Gaussian channels: definitions and some exact results

TL;DR

This paper formulates a generalized conjecture for minimal output entropy in Gaussian channels, proposing that Gaussian states minimize output entropy for fixed input entropy, and proves it in specific cases.

Contribution

It introduces a new generalized conjecture for Gaussian channels and provides proofs for certain special cases, advancing understanding of entropy minimization.

Findings

Conjecture holds for centered Gaussian channels in specific cases.

Thermal states minimize output entropy in centered channels.

Provides a framework for future proofs of the conjecture.

Abstract

A formulation of the generalized minimal output entropy conjecture for Gaussian channels is presented. It asserts that, for states with fixed input entropy, the minimal value of the output entropy of the channel (i.e. the minimal output entropy increment for fixed input entropy) is achieved by Gaussian states. In the case of centered channels (i.e. channels which do not add squeezing to the input state) this implies that the minimum is obtained by thermal (Gibbs) inputs. The conjecture is proved to be valid in some special cases.