Catalytic Transformations in Coherence Theory

TL;DR

This paper establishes the operational significance of various coherence measures in single-copy quantum systems using catalysts, connecting asymptotic and catalytic transformations and analyzing key protocols.

Contribution

It provides the first clear operational interpretation of relative entropy of coherence and coherence of formation in single-copy setups via catalysts.

Findings

Operational meaning of coherence measures established in single-copy context.

Existence of correspondence between asymptotic and catalytic transformations proved.

Analysis of assisted distillation and quantum incoherent state merging protocols.

Abstract

In 2016, A. Winter et al.(Physical Review Letters 116 (12) (2016) 120404) provided an operational meaning to relative entropy of coherence and coherence of formation by introducing coherence distillation and dilation protocol in asymptotic setup. Though relative entropy of coherence introduced in 2014 by T. Baumgratz ( Physical Review Letters 113 (14) (2014) 140401) as a coherence measure but it's operational meaning in single copy setup was unknown so far. Here we have provided relative entropy of coherence (via IO (Incoherent Operations)) and coherence of formation (via IO) and quantum incoherent relative entropy (via LQICC(Local Quantum Incoherent Operations with Classical Communications)) a clear operational significance in single copy setup using the concept of catalyst. We have proved an existential correspondence between asymptotic and catalytic state transformation using IO, LICC(Local Incoherent Operations with Classical Communications) and LQICC. We have also discussed two very important protocols, assisted distillation and quantum incoherent state merging, in single copy setup using catalyst. Monotone property of relative entropy of coherence, coherence of formation and quantum incoherent relative entropy under the catalytic transformation are also discussed here.