Coherence manipulation under non-cohering operations

Abstract

In this paper, we consider the coherence manipulation in the limit of arbitrarily many copies of the states under operations which generate a negligible amount of coherence. Meanwhile, it allows us to define the distillable coherence and coherence cost under asymptotically non-cohering operations. We show that the two quantifiers are equal to the relative entropy of coherence, which is identified as the regularized and smoothed version of the logarithmic robustness of coherence; this shows that the coherence can be interconverted reversibly. We also show that any two coherence states are reversible under asymptotically non-cohering operations with a rate given by the ration of the relative entropy of coherence.