Fundamental Limits on Correlated Catalytic State Transformations

TL;DR

This paper establishes fundamental limits on correlated catalytic state transformations, showing that minimal residual correlations require highly resourceful catalysts, with implications across various quantum resource theories.

Contribution

It proves that small residual correlations in catalytic transformations necessitate highly resourceful catalysts, revealing limits on catalyst efficiency in resource theories.

Findings

Small residual correlations imply highly resourceful catalysts.

Resource requirements diverge as residual correlation approaches zero.

Results apply broadly across thermality, coherence, and entanglement theories.

Abstract

Determining whether a given state can be transformed into a target state using free operations is one of the fundamental questions in the study of resources theories. Free operations in resource theories can be enhanced by allowing for a catalyst system that assists the transformation and is returned unchanged, but potentially correlated, with the target state. While this has been an active area of recent research, very little is known about the necessary properties of such catalysts. Here, we prove fundamental limits applicable to a large class of correlated catalytic transformations by showing that a small residual correlation between catalyst and target state implies that the catalyst needs to be highly resourceful. In fact, the resources required diverge in the limit of vanishing residual correlation. In addition, we establish that in imperfect catalysis a small error generally implies a highly resourceful embezzling catalyst. We develop our results in a general resource theory framework and discuss its implications for the resource theory of athermality, the resource theory of coherence and entanglement theory.