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arXiv:1707.07974 · Journal of Physics A Mathematical and Theoretical

On two recent proposals for witnessing nonclassical gravity

Michael J. W. Hall, Marcel Reginatto

Published Jan 12, 2018• 74 citations
arXivHTMLPDF

Abstract

Abstract Two very similar proposals have been made recently for witnessing nonclassical features of gravity, by Bose et al and by Marletto and Vedral. However, while these proposals are asserted to be very general, they are in fact based on a very strong claim: that quantum systems cannot become entangled via a classical intermediary. We point out that the support provided for this claim is only applicable to a very limited class of quantum-classical interaction models, corresponding to Koopman-type dynamics. We show that the claim is also valid for mean-field models, but that it is contradicted by explicit counterexamples based on the configuration-ensemble model. Thus, neither proposal provides a definitive test of nonclassical gravity.

DOI
10.1088/1751-8121/aaa734

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Abstract Two very similar proposals have been made recently for witnessing nonclassical features of gravity, by Bose et al and by Marletto and Vedral. However, while these proposals are asserted to be very general, they are in fact based on a very strong claim: that quantum systems cannot become entangled via a classical intermediary. We point out that the support provided for this claim is only applicable to a very limited class of quantum-classical interaction models, corresponding to Koopman-type dynamics. We show that the claim is also valid for mean-field models, but that it is contradicted by explicit counterexamples based on the configuration-ensemble model. Thus, neither proposal provides a definitive test of nonclassical gravity.
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.
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.
Recently, Vedral and one of us proposed an entanglement-based witness of non-classicality in systems that need not obey quantum theory, based on information-theoretic ideas [ 1 , 3 ], which offers a robust foundation for newly proposed table-top tests of non-classicality in gravity, [ 2 , 3 ]. The witness asserts that if a mediator can entangle locally two quantum systems, then it has to be non-classical. Hall and Reginatto [ 4 , 7 ] claimed that there are classical systems that can entangle two quantum systems, thus violating our proposed witness. Here we refute that claim, explaining that the counterexample proposed by Hall and Reginatto in fact validates the witness, vindicating the witness of non-classicality in its full generality.
Abstract Bose et al and Marletto and Vedral proposed an experiment to test whether gravity can induce entanglement between massive systems, arguing that the capacity to do so would imply the quantum nature of gravity. In this work, a class of semi-classical models is examined that treat gravity classically, through some potential in the Schrödinger equation, and it is shown that these models do not generate entanglement. This class includes the Newton–Schrödinger model, where gravity is sourced by the wave function, the Bohmian analogue, where gravity is sourced by actual point-particles, and an interpolating model proposed by Döner and Großardt. These models are analyzed in the context of the proposed experiment and contrasted with the standard Newtonian potential, which does generate entanglement.
Abstract There has been a wave of recent interest in detecting the quantum nature of gravity with tabletop 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 modeled 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 modeling 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.
Abstract Experiments witnessing the entanglement between two particles interacting only via the gravitational field have been proposed as a test whether gravity must be quantized. In the language of quantum information, a non-quantum gravitational force would be modeled by local operations with classical communication (LOCC), which cannot generate entanglement in an initially unentangled state. This idea is criticized as too constraining on possible alternatives to quantum gravity. We present a parametrized model for the gravitational interaction of quantum matter on a classical spacetime, inspired by the de Broglie–Bohm formulation of quantum mechanics, which results in entanglement and thereby provides an explicit counterexample to the claim that only a quantized gravitational field possesses this capability.