# Dequantization via quantum channels

June 04, 2015

For a unital completely positive map $\Phi$ ("quantum channel") governing the
time propagation of a quantum system, the Stinespring representation gives an
enlarged system evolving unitarily. We argue that the Stinespring
representations of each power $\Phi^m$ of the single map together encode the
structure of the original quantum channel and provides an interaction-dependent
model for the bath. The same bath model gives a "classical limit" at infinite
time $m\to\infty$ in the form of a noncommutative "manifold" determined by the
channel. In this way a simplified analysis of the system can be performed by
making the large-$m$ approximation. These constructions are based on a
noncommutative generalization of Berezin quantization. The latter is shown to
involve very fundamental aspects of quantum-information theory, which are
thereby put in a completely new light.

open access link
Lett Math Phys 106(10), 1397-1414 (2016)

@article{Andersson:2016fwq,
author = "Andersson, Andreas",
title = "{Dequantization Via Quantum Channels}",
journal = "Lett. Math. Phys.",
volume = "106",
year = "2016",
number = "10",
pages = "1397-1414",
doi = "10.1007/s11005-016-0874-2",
eprint = "1506.01453",
archivePrefix = "arXiv",
primaryClass = "math-ph",
SLACcitation = "%%CITATION = ARXIV:1506.01453;%%"
}

Keywords:

*none*