Coherence generating power of quantum dephasing processes

We provide a quantification of the capability of various quantum dephasing processes to generate coherence out of incoherent states. The measures defined, admitting computable expressions for any finite Hilbert space dimension, are based on probabilistic averages and arise naturally from the viewpoint of coherence as a resource. We investigate how the capability of a dephasing process (e.g., a non-selective orthogonal measurement) to generate coherence depends on the relevant bases of the Hilbert space over which coherence is quantified and the dephasing process occurs, respectively. We extend our analysis to include those Lindblad time evolutions which, in the infinite time limit, dephase the system under consideration and calculate their coherence generating power as a function of time. We further identify specific families of such time evolutions that, although dephasing, have optimal (over all quantum processes) coherence generating power for some intermediate time. Finally, we investigate the coherence generating capability of random dephasing channels.