Catalytic Gaussian thermal operations

TL;DR

This paper investigates how catalysts can enhance state transformations in Gaussian thermal operations, revealing that weak catalysts enable more transformations than strong ones, with implications for Gaussian-based devices.

Contribution

It introduces a parametrisation of covariance matrices and establishes conditions under which weak catalysts expand the set of reachable states in Gaussian thermal resource theory.

Findings

Strong catalysts do not expand state reachability in single-mode cases.

Weak catalysts enable additional state transformations.

Necessary conditions for multi-mode transformations are derived.

Abstract

We examine the problem of state transformations in the framework of Gaussian thermal resource theory in the presence of catalysts. To this end, we introduce an expedient parametrisation of covariance matrices in terms of principal mode temperatures and asymmetries, and consider both weak and strong catalytic scenarios. We show that strong catalysts (where final correlations with the system are forbidden) are useless for the single mode case, in that they do not expand the set of states reachable from a given initial state through Gaussian thermal operations. We then go on to prove that weak catalysts (where final correlations with the system are allowed) are instead capable of reaching more final system states, and determine exact conditions for state transformations of a single-mode in their presence. Next, we derive necessary conditions for Gaussian thermal state transformations holding for any number of modes, for strong catalysts and approximate transformations, and for weak catalysts with and without the addition of a thermal bath. We discuss the implications of these results for devices operating with Gaussian elements.