Catalytic coherence transformations

TL;DR

This paper characterizes the conditions under which quantum coherence transformations can be catalyzed by auxiliary systems, including deterministic, stochastic, and self-catalytic cases, expanding understanding of coherence manipulation.

Contribution

It provides the first complete characterization of catalytic coherence transformations between pure states, including necessary and sufficient conditions for various types of transformations.

Findings

Necessary and sufficient conditions for deterministic catalytic coherence transformations.

Conditions for stochastic catalytic coherence transformations with higher success probabilities.

Demonstration of self-catalysis and entanglement-assisted coherence transformations.

Abstract

Catalytic coherence transformations allow the otherwise impossible state transformations using only incoherent operations with the aid of an auxiliary system with finite coherence which is not being consumed in anyway. Here we find the necessary and sufficient conditions for the deterministic and stochastic catalytic coherence transformations between pair of pure quantum states. In particular, we show that the simultaneous decrease of a family of R\'enyi entropies of the diagonal parts of the states under consideration are necessary and sufficient conditions for the deterministic catalytic coherence transformations. Similarly, for stochastic catalytic coherence transformations we find the necessary and sufficient conditions for achieving higher optimal probability of conversion. We, thus, completely characterize the coherence transformations amongst pure quantum states under incoherent operations. We give numerous examples to elaborate our results. We also explore the possibility of the same system acting as a catalyst for itself and find that indeed {\it self catalysis} is possible. Further, for the cases where no catalytic coherence transformation is possible we provide entanglement assisted coherence transformations and find the necessary and sufficient conditions for such transformations.