Dephasing superchannels

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