Dequantization via quantum channels

Andreas Andersson
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;%%" }