Catalytic transformations in coherence theory

Abstract

In 2016, Winter and Yang [A. Winter and D. Yang, Phys. Rev. Lett. 116, 120404 (2016)] provided an operational meaning to relative entropy of coherence and coherence of formation by introducing coherence distillation and dilation protocols in an asymptotic setup. Here we have provided relative entropy of coherence [via incoherent operations (IO)] and coherence of formation (via IO) and quantum incoherent relative entropy [via local quantum incoherent operations with classical communications (LQICC)] as a measure using the concept of a catalyst. We have proved an existential correspondence between asymptotic and catalytic state transformation using IO, local incoherent operations with classical communications, and LQICC. We have also discussed two very important protocols, assisted distillation and quantum incoherent state merging using a catalyst. Monotone properties of relative entropy of coherence, coherence of formation, and quantum incoherent relative entropy under the catalytic transformation are also discussed here.