Covariant catalysis requires correlations and good quantum reference frames degrade little

TL;DR

This paper investigates the role of correlations and quantum reference frames in covariant catalysis, showing that effective catalysts must build correlations and that high-precision simulation minimally degrades the reference frame.

Contribution

It provides new insights into the necessity of correlations for covariant catalysts and demonstrates that high-precision simulations preserve the integrity of quantum reference frames.

Findings

Exact catalysts must build correlations to be useful.

Pure state catalysts are ineffective due to lack of correlations.

High-precision simulation minimally degrades quantum reference frames.

Abstract

Catalysts are quantum systems that open up dynamical pathways between quantum states which are otherwise inaccessible under a given set of operational restrictions while, at the same time, they do not change their quantum state. We here consider the restrictions imposed by symmetries and conservation laws, where any quantum channel has to be covariant with respect to the unitary representation of a symmetry group, and present two results. First, for an exact catalyst to be useful, it has to build up correlations to either the system of interest or the degrees of freedom dilating the given process to covariant unitary dynamics. This explains why catalysts in pure states are useless. Second, if a quantum system ("reference frame") is used to simulate to high precision unitary dynamics (which possibly violates the conservation law) on another system via a global, covariant quantum channel, then this channel can be chosen so that the reference frame is approximately catalytic. In other words, a reference frame that simulates unitary dynamics to high precision degrades only very little.