Strong* convergence of quantum channels

Abstract

In [arXiv:1712.03219] the existence of a strongly (pointwise) converging sequence of quantum channels that can not be represented as a reduction of a sequence of unitary channels strongly converging to a unitary channel is shown. In this work we give a simple characterization of sequences of quantum channels that have the above representation. The corresponding convergence is called the strong* convergence, since it is related to the convergence of selective Stinespring isometries of quantum channels in the strong* operator topology. Some properties of the strong* convergence of quantum channels are considered. It is shown that for Bosonic Gaussian channels the strong* convergence coincides with the strong convergence.