Hybrid classical-quantum formulations ask for hybrid notions

TL;DR

This paper critically examines hybrid classical-quantum models, revealing that they inherently involve additional degrees of freedom and exchange of quantumness, challenging their physical consistency.

Contribution

It reanalyzes hybrid models to identify common features and clarifies the necessity of extra degrees of freedom and the exchange of classical and quantum properties.

Findings

Hybrid models require extra degrees of freedom.

Subsystems in hybrid systems are never purely classical or quantum.

Quantumness is exchanged between sectors in hybrid models.

Abstract

We reappraise some of the hybrid classical-quantum models proposed in the literature with the goal of retrieving some of their common characteristics. In particular, first, we analyze in detail the Peres-Terno argument regarding the inconsistency of hybrid quantizations of the Sudarshan type. We show that to accept such hybrid formalism entails the necessity of dealing with additional degrees of freedom beyond those in the straight complete quantization of the system. Second, we recover a similar enlargement of degrees of freedom in the so-called statistical hybrid models. Finally, we use Wigner's quantization of a simple model to illustrate how in hybrid systems the subsystems are never purely classical or quantum. A certain degree of quantumness (classicality) is being exchanged between the different sectors of the theory, which in this particular unphysical toy model makes them undistinguishable.