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.
Keywords
Cite
@article{arxiv.1802.05632,
title = {Strong* convergence of quantum channels},
author = {M. E. Shirokov},
journal= {arXiv preprint arXiv:1802.05632},
year = {2021}
}
Comments
18 pages, this is a strengthened extension of sections 6 and 7 from the previous version of arXiv:1712.03219, in v2 minor corrections are made and the case of Gaussian channels is added, any comments are welcome