A model-theoretic interpretation of environmentally-induced superselection

TL;DR

The paper critically examines environmentally-induced superselection, demonstrating it cannot independently produce classical systems without assuming a classical environment, and reinterprets it using POVMs as virtual machines aligned with classical computation.

Contribution

It shows that einselection requires a classical environment to produce classicality and offers a POVM-based reformulation interpreting classical systems as virtual machines.

Findings

Einselection depends on a classical environment to generate classical systems.

Reformulation of einselection using POVMs provides a new interpretation.

Classical systems can be viewed as virtual machines without extra assumptions.

Abstract

Environmentally-induced superselection or "einselection" has been proposed as an observer-independent mechanism by which apparently classical systems "emerge" from physical interactions between degrees of freedom described completely quantum-mechanically. It is shown that einselection can only generate classical systems if the "environment" is assumed \textit{a priori} to be classical; einselection therefore does not provide an observer-independent mechanism by which classicality can emerge from quantum dynamics. Einselection is then reformulated in terms of positive operator-valued measures (POVMs) acting on a global quantum state. It is shown that this re-formulation enables a natural interpretation of apparently-classical systems as virtual machines that requires no assumptions beyond those of classical computer science.