Entanglement of quantum systems via a classical mediator in hybrid van Hove theory

TL;DR

This paper demonstrates that entanglement between quantum systems can occur via a classical mediator within hybrid van Hove theory, challenging no-go theorems and impacting the interpretation of quantum gravity experiments.

Contribution

It shows that entanglement can be generated through a classical mediator in hybrid quantum-classical theories, specifically within the hybrid van Hove framework, contrary to previous no-go results.

Findings

Entanglement is possible via a classical mediator in hybrid van Hove theory.

The spin density matrix analysis confirms entanglement generation.

Quantum entanglement studies cannot exclude classical gravity theories.

Abstract

It is a matter of ongoing discussion whether quantum states can become entangled while only interacting via a classical mediator. This lively debate is deeply interwoven with the question of whether entanglement studies can prove the quantum nature of gravity. However, the answer to this fundamental question depends crucially on which hybrid quantum-classical theory is used. In this letter, we demonstrate that entanglement by a classical mediator is possible within the framework of hybrid van Hove theory, showing that existing no-go theorems on that matter do not universally apply to hybrid theories in general. After briefly recapitulating the key features of the hybrid van Hove theory, we show this using the example of two quantum spins coupled by a classical harmonic oscillator. By deriving the spin density matrix for this scenario and comparing it to its equivalent for a pure quantum system, we show that entanglement between the two spins is generated in both cases. Conclusively, this is illustrated by presenting the purity and concurrence of the spin-spin system as a decisive measure for entanglement. Our results further imply that quantum entanglement studies cannot rule out consistent quantum theories featuring classical gravity.