Dephasing superchannels

We characterise a class of environmental noises that decrease coherent properties of quantum channels by introducing and analysing the properties of dephasing superchannels. These are defined as superchannels that affect only non-classical properties of a quantum channel mathcal{E}, i.e., they leave invariant the transition probabilities induced by mathcal{E} in the distinguished basis. We prove that such superchannels Ξ_C form a particular subclass of Schur-product supermaps that act on the Jamiolkowski state J\(mathcal{E}\) of a channel mathcal{E} via a Schur product, J'=Jcirc C. We also find physical realizations of general Ξ_C through a pre- and post-processing employing dephasing channels with memory, and show that memory plays a non-trivial role for quantum systems of dimension d>2. Moreover, we prove that coherence generating power of a general quantum channel is a monotone under dephasing superchannels. Finally, we analyse the effect dephasing noise can have on a quantum channel mathcal{E} by investigating the number of distinguishable channels that mathcal{E} can be mapped to by a family of dephasing superchannels. More precisely, we upper bound this number in terms of hypothesis testing channel divergence between mathcal{E} and its fully dephased version, and also relate it to the robustness of coherence of mathcal{E}.