Catalytic Gaussian thermal operations

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.

Automated summary

In this study, the problem of state transformations in the presence of catalysts is examined within the framework of Gaussian thermal resource theory. The results show that strong catalysts are ineffective for the single mode case, while weak catalysts can achieve more final system states. Necessary conditions for Gaussian thermal state transformations are derived for different numbers of modes, including strong catalysts, approximate transformations, and weak catalysts with and without a thermal bath.