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arXiv:2601.21555

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

Sebastian Ulbricht, Andrés Darío Bermúdez Manjarres, Marcel Reginatto

quant-phSubmitted Jan 29, 2026• Announced Jan 30, 2026• 0 citations
v1 · Jan 29, 2026v2 · Oct 1, 2026
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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.

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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.
Recently, table-top experiments involving massive quantum systems have been proposed to test the interface of quantum theory and gravity. In particular, the crucial point of the debate is whether it is possible to conclude anything on the quantum nature of the gravitational field, provided that two quantum systems become entangled solely due to the gravitational interaction. Typically, this question has been addressed by assuming a specific physical theory to describe the gravitational interaction, but no systematic approach to characterise the set of possible gravitational theories which are compatible with the observation of entanglement has been proposed. Here, we remedy this by introducing the framework of Generalised Probabilistic Theories (GPTs) to the study of the nature of the gravitational field. This framework enables us to systematically study all theories compatible with the detection of entanglement generated via the gravitational interaction between two systems. We prove a no-go theorem stating that the following statements are incompatible: i) gravity is able to generate entanglement; ii) gravity mediates the interaction between the systems; iii) gravity is classical. We analyse the violation of each condition, in particular with respect to alternative non-linear models such as the Schrödinger-Newton equation and Collapse Models.
Motivated by models of mixed quantum-classical hybrid theories, we consider the representation of classical observables as Hilbert-space operators based on van Hove's unitary representation of contact transformations. This leads to a reformulation of classical mechanics where the phase space density satisfies the Liouville equation and, more importantly, classical observables are represented by van Hove operators that satisfy a commutation algebra isomorphic to the classical Poisson algebra of functions in phase space. Thus, this Hilbert space approach captures all the essential features of the phase space formulation of classical mechanics in that it reproduces its algebraic structure -- something that is not achieved by other approaches such as the Koopman-von Neumann theory. As an important feature, the definition of appropriate physical states in this formalism imposes certain natural requirements on the phase of the classical wave function, which ensure correct expectation values for the observables. Furthermore, we discuss how to extend the approach to the hybrid van Hove theory of mixed classical-quantum systems and illustrate its application with the example of interacting classical and quantum oscillators. Finally, we focus on the question of how hybrid van Hove theory evades no-go theorems on mixed classical-quantum systems and point to the various assumptions of the no-go theorems that do not apply to our approach. This demonstrates that these no-go theorems are not universally applicable, contrary to their original claims.
A recent paper by Aziz and Howl (Nature 2025) argues that, once quantum matter is described at the level of quantum field theory and coupled to a classical gravitational field, higher order processes can generate entanglement between two spatially separated masses. A contemporaneous critical note (Marletto, Oppenheim, Vedral, Wilson, arXiv:2511.07348v1) shows that, in the actual nonrelativistic limit employed there, the interaction becomes ultra local, the total unitary factorizes, and no entanglement is generated from a product input. In this comment we (i) restate the core point of that critique, (ii) give a channel theoretic reformulation that makes the conclusion model independent, and (iii) clarify the distinction between activation of entanglement in already quantum matter and genuine mediation of entanglement by a classical field. Once these clarifications are in place, the standard BMV inference that observation of gravity mediated entanglement strongly indicates nonclassical gravitational degrees of freedom remains intact.
We consider two interacting systems when one is treated classically while the other system remains quantum. Consistent dynamics of this coupling has been shown to exist, and explored in the context of treating space-time classically. Here, we prove that any such hybrid dynamics necessarily results in decoherence of the quantum system, and a breakdown in predictability in the classical phase space. We further prove that a trade-off between the rate of this decoherence and the degree of diffusion induced in the classical system is a general feature of all classical quantum dynamics; long coherence times require strong diffusion in phase-space relative to the strength of the coupling. Applying the trade-off relation to gravity, we find a relationship between the strength of gravitationally-induced decoherence versus diffusion of the metric and its conjugate momenta. This provides an experimental signature of theories in which gravity is fundamentally classical. Bounds on decoherence rates arising from current interferometry experiments, combined with precision measurements of mass, place significant restrictions on theories where Einstein's classical theory of gravity interacts with quantum matter. We find that part of the parameter space of such theories are already squeezed out, and provide figures of merit which can be used in future mass measurements and interference experiments.
We consider two interacting systems when one is treated classically while the other system remains quantum. Consistent dynamics of this coupling has been shown to exist, and explored in the context of treating space-time classically. Here, we prove that such hybrid dynamics necessarily results in decoherence of the quantum system, and a breakdown in predictability in the classical phase space. We further prove that a trade-off between the rate of this decoherence and the degree of diffusion induced in the classical system is a general feature of all classical quantum dynamics; long coherence times require strong diffusion in phase-space relative to the strength of the coupling. Applying the trade-off relation to gravity, we find a relationship between the strength of gravitationally-induced decoherence versus diffusion of the metric and its conjugate momenta. This provides an experimental signature of theories in which gravity is fundamentally classical. Bounds on decoherence rates arising from current interferometry experiments, combined with precision measurements of mass, place significant restrictions on theories where Einstein's classical theory of gravity interacts with quantum matter. We find that part of the parameter space of such theories are already squeezed out, and provide figures of merit which can be used in future mass measurements and interference experiments.
Models of quantum-classical interactions fall into two classes: those which allow the generation of quantum entanglement via a classical mediator (such as gravity), and those which do not. Marconato and Marletto have recently sought to distinguish between these classes by claiming that known members of the first class (based on the configuration-ensemble formalism introduced by us) fail to model the mediator as a 'classical' system, and are nonlocal. We explicitly show that this claim is incorrect, and expose a large number of errors and misconceptions in their reasoning. We also point to a very simple and transparent example of the generation of entanglement between two qubits via a classical bit. It follows that there are models permitting the generation of entanglement via quantum-classical interactions that lie outside the remit of the theorem cited by Marconato and Marletto. We clarify the reasons for the limited applicability of various no-go theorems for entanglement generation.