Proliferation of observables and measurement in quantum-classical hybrids

TL;DR

This paper explores the complex structure of observables in quantum-classical hybrid systems, emphasizing how hybridization affects measurement, superposition, and entanglement, while maintaining locality and non-signalling.

Contribution

It introduces a framework for QM-CL hybrids that extends classical mechanics to include quantum features, addressing the proliferation of observables and their measurement implications.

Findings

Hybrid observables form a larger set than component observables

Quantumness and classicality influence each other in hybrids

The framework supports superposition, entanglement, and local non-signalling

Abstract

Following a review of quantum-classical hybrid dynamics, we discuss the ensuing proliferation of observables and relate it to measurements of (would-be) quantum mechanical degrees of freedom performed by (would-be) classical ones (if they were separable). -- Hybrids consist in coupled classical ("CL") and quantum mechanical ("QM") objects. Numerous consistency requirements for their description have been discussed and are fulfilled here. We summarize a representation of quantum mechanics in terms of classical analytical mechanics which is naturally extended to QM-CL hybrids. This framework allows for superposition, separable, and entangled states originating in the QM sector, admits experimenter's "Free Will", and is local and non-signalling. -- Presently, we study the set of hybrid observables, which is larger than the Cartesian product of QM and CL observables of its components; yet it is smaller than a corresponding product of all-classical observables. Thus, quantumness and classicality infect each other.