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.

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

References in corpus (5)

• Multi-mode bosonic Gaussian channels
• Energy-constrained diamond norm with applications to the uniform continuity of continuous variable channel capacities
• Strong and uniform convergence in the teleportation simulation of bosonic Gaussian channels
• Strong convergence of quantum channels: continuity of the Stinespring dilation and discontinuity of the unitary dilation
• The Information-Disturbance Tradeoff and the Continuity of Stinespring's Representation

Cited by in corpus (2)

• Quantum relative entropy: general convergence criterion and preservation of convergence under completely positive linear maps
• Progress on the Kretschmann-Schlingemann-Werner Conjecture