Catalytic transformations in coherence theory

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