Gravity-mediated entanglement via infinite-dimensional systems (2507.13201v1)

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.

• The paper shows that classical gravity, modeled via infinite-dimensional commutative C*-algebras, cannot mediate quantum entanglement.
• It uses a rigorous framework with local interactions and triseparable states to prove that classical mediators preserve separability.
• The findings imply that any observed gravitational entanglement requires quantum characteristics, supporting the search for quantum gravity.

Gravity-Mediated Entanglement via Infinite-Dimensional Systems

Introduction

The paper explores the possibility of detecting the quantum nature of gravity through tabletop experiments designed to observe gravitationally mediated entanglement (GME). These experiments aim to provide evidence of the non-classical nature of gravity by demonstrating that entanglement between two masses can be induced solely through gravitational interactions. Traditional approaches assume such mediation must possess non-classical attributes if entanglement is observed. However, previous models simplify classical mediators as finite, discrete systems, excluding continuous and infinite-dimensional systems like those in classical mechanics and field theory.

Classical Systems and $C^*$-Algebras

The paper addresses this gap by modeling classical systems using commutative unital $C^*$-algebras. These algebras represent a broad class of potentially relevant physical systems, including infinite-dimensional ones. Classical systems characterized by these algebras do not mediate entanglement between quantum systems, even when the quantum systems are infinite-dimensional or are described using arbitrary $C^*$-algebras, such as those in Quantum Field Theory.

Description Using $C^*$-Algebras

Classical and quantum physics can be framed using $C^*$-algebras, where classical systems correspond to commutative algebras. For finite classical configuration spaces, functions form vector spaces and algebras, with $C^*$-algebras providing a robust foundation. Infinite-dimensional commutative algebras, related to continuous functions on specific spaces, represent general classical systems, accommodating bounded sequences or functions, reinforcing classical physics descriptions.

No Entanglement Mediation

Setup and Interaction

The paper considers a scenario with two quantum systems, $A$ and $B$, and a classical mediator $G$. The interaction is local, meaning either $A$ or $B$ can interact with $G$ in each round, but not simultaneously. The system is modeled mathematically using unital $C^*$-algebras, describing quantum and classical systems, and a tensor product representing the composite systems.

Triseparable States

The initial state of the system is prepared independently, represented by product states, a form of triseparable states. The paper demonstrates that local interactions via classical systems preserve the triseparability of states, concluding that classical systems like $G$ cannot mediate entanglement. This result is proven by showing that channels representing local interactions map triseparable states to themselves.

Discussion

This work generalizes previous results by extending the arguments to infinite-dimensional mediators, thereby accommodating more realistic classical systems. It suggests that any observed entanglement via gravity requires the gravitational field to possess non-classical properties, opposing purely classical interpretations.

Implications and Comparisons

The paper reinforces that the detection of entanglement indicates necessitate non-classical features of gravity, such as non-commutativity or quantum field behavior. Comparisons with other theoretical frameworks show that even operator-algebraic descriptions accommodate this non-classical requirement, aligning with recent findings in quantum gravity experiments and quantum field theories.

Conclusion

The paper closes a significant gap in existing research by ruling out the possibility of classical gravity mediation for entanglement, especially emphasizing infinite-dimensional, continuous models. These findings underscore the necessity for gravity to exhibit quantum characteristics, promoting further experiments that could probe the quantum nature of gravity more definitively.