Gravity-mediated entanglement via infinite-dimensional systems

TL;DR

This paper demonstrates that classical infinite-dimensional systems cannot mediate entanglement between quantum systems, supporting the idea that gravity-induced entanglement implies gravity's non-classical nature.

Contribution

It extends previous models by including infinite-dimensional classical systems, showing they cannot generate entanglement, thus strengthening the argument for gravity's quantum properties.

Findings

Classical systems modeled as commutative C*-algebras cannot mediate entanglement.

The result holds even for infinite-dimensional or quantum field theoretic systems.

Supports the necessity of non-classical features in gravity for entanglement generation.

Abstract

There has been a wave of recent interest in detecting the quantum nature of gravity with table-top experiments that witness gravitationally mediated entanglement. Central to these proposals is the assumption that any mediator capable of generating entanglement must itself be nonclassical. However, previous arguments for this have modelled classical mediators as finite, discrete systems such as bits, which excludes physically relevant continuous and infinite-dimensional systems such as those of classical mechanics and field theory. In this work, we close this gap by modelling classical systems as commutative unital C*-algebras, arguably encompassing all potentially physically relevant classical systems. We show that these systems cannot mediate entanglement between two quantum systems A and B, even if A and B are themselves infinite-dimensional or described by arbitrary unital C*-algebras (as in Quantum Field Theory), composed with an arbitrary C*-tensor product. This result reinforces the conclusion that the observation of gravity-induced entanglement would require the gravitational field to possess inherently non-classical features.