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 $\Xi_C$ 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, $J'=J\circ C$. We also find physical realizations of general $\Xi_C$ 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 $\mathcal{ E}$.
Categories: quant-ph