Dephasing superchannels
Abstract
We characterize a class of environmental noises that decrease the coherent properties of quantum channels by introducing and analyzing the properties of dephasing superchannels. These are defined as superchannels that affect only nonclassical properties of a quantum channel E , i.e., they leave invariant the transition probabilities induced by E in the distinguished basis. We prove that such superchannels Ξ_{C} form a particular subclass of Schurproduct supermaps that act on the Jamiołkowski state J (E ) of a channel E via a Schur product, J^{'}=J ∘C . We also find physical realizations of general Ξ_{C} through pre and postprocessing employing dephasing channels with memory, and we show that memory plays a nontrivial role for quantum systems of dimension d >2 . Moreover, we prove that the coherencegenerating power of a general quantum channel is a monotone under dephasing superchannels. Finally, we analyze the effect that dephasing noise can have on a quantum channel E by investigating the number of distinguishable channels that E can be mapped to by a family of dephasing superchannels. More precisely, we upperbound this number in terms of hypothesistesting channel divergence between E and its fully dephased version, and we also relate it to the robustness of coherence of E .
 Publication:

Physical Review A
 Pub Date:
 November 2021
 DOI:
 10.1103/PhysRevA.104.052611
 arXiv:
 arXiv:2107.06585
 Bibcode:
 2021PhRvA.104e2611P
 Keywords:

 Quantum Physics
 EPrint:
 13 pages, 1 figure. Published version