| Abstract |
<p>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 <em>E</em>, i.e., they leave invariant the transition probabilities induced by <em>E</em> in the distinguished basis. We prove that such superchannels ΞC form a particular subclass of Schur-product supermaps that act on the Jamiolkowski state J(<em>E</em>) of a channel <em>E</em> via a Schur product, J′=J∘C. We also find physical realizations of general ΞC 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 <em>E</em> by investigating the number of distinguishable channels that <em>E</em> 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 <em>E</em> and its fully dephased version, and also relate it to the robustness of coherence of <em>E</em>.</p>
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