Dequantization via quantum channels
For a unital completely positive map Φ ("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 Φm of the single map together encode the structure of the original quantum channel and provide an interaction-dependent model for the bath. The same bath model gives a "classical limit" at infinite time m-∞ 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.