Dong Yang, University of Barcelona
From the viewpoint of resource theory, we establish the coherence
theory in an operational way. Namely we introduce the two basic concepts
— “coherence distillation” and “coherence cost” in the coherence
transformation processing and show that the evaluations of them are
reduced to single-letter formula: the coherence distillation is given by
the relative entropy of coherence (or in other words, we give the
relative entropy of coherence its operational interpretation) and the
coherence cost by the coherence formation which involves just the
optimization. An immediate corollary is that there exists no bound
coherent state in the sense that it is needed to consume coherence to
create the state but no coherence can be distilled from it. Further we
demonstrate that the coherence theory is generically an irreversible
theory by a simple criterion that completely characterizes all the
reversible coherent states.