Dequantization via quantum channels

TL;DR

This paper explores how the Stinespring representations of powers of a quantum channel encode the system's structure and bath interactions, revealing a classical limit and connecting to noncommutative Berezin quantization.

Contribution

It introduces a novel approach to analyze quantum channels through their powers' Stinespring representations, linking quantum information theory with noncommutative geometry.

Findings

Stinespring representations encode the structure of quantum channels.

A classical limit emerges at infinite time, modeled by a noncommutative manifold.

Connections established between quantum information theory and Berezin quantization.

Abstract

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.