Strong* convergence of quantum channels

TL;DR

This paper characterizes the strong* convergence of quantum channels, relating it to the convergence of Stinespring isometries, and shows that for Bosonic Gaussian channels, strong* convergence coincides with strong convergence.

Contribution

It provides a simple characterization of sequences of quantum channels with strong* convergence and explores its properties, especially for Bosonic Gaussian channels.

Findings

Strong* convergence relates to convergence of Stinespring isometries.

For Bosonic Gaussian channels, strong* and strong convergence are equivalent.

The paper offers insights into the structure of quantum channel convergence.

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.