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arXiv:2302.03075 · Physical Review X

Testing the Quantumness of Gravity without Entanglement

Ludovico Lami, Julen Simon Pedernales, Martin Bodo Plenio

Published May 1, 2024• 32 citations
arXivHTMLPDF

Abstract

Given a unitary evolution U on a multipartite quantum system and an ensemble of initial states, how well can U be simulated by local operations and classical communication (LOCC) on that ensemble? We answer this question by establishing a general, efficiently computable upper bound on the maximal LOCC simulation fidelity—what we call an “LOCC inequality.” We then apply our findings to the fundamental setting where U implements a quantum Newtonian Hamiltonian over a gravitationally interacting system. Violation of our LOCC inequality can rule out the LOCCness of the underlying evolution, thereby establishing the nonclassicality of the gravitational dynamics, which can no longer be explained by a local classical field. As a prominent application of this scheme we study systems of quantum harmonic oscillators initialized in coherent states following a normal distribution and interacting via Newtonian gravity, and discuss a possible physical implementation with torsion pendula. One of our main technical contributions is the analytical calculation of the above LOCC inequality for this family of systems. As opposed to existing tests based on the detection of gravitationally mediated entanglement, our proposal works with coherent states alone, and thus it does not require the generation of largely delocalized states of motion nor the detection of entanglement, which is never created at any point in the process. Published by the American Physical Society 2024

DOI
10.1103/physrevx.14.021022

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Given a unitary evolution U on a multipartite quantum system and an ensemble of initial states, how well can U be simulated by local operations and classical communication (LOCC) on that ensemble? We answer this question by establishing a general, efficiently computable upper bound on the maximal LOCC simulation fidelity—what we call an “LOCC inequality.” We then apply our findings to the fundamental setting where U implements a quantum Newtonian Hamiltonian over a gravitationally interacting system. Violation of our LOCC inequality can rule out the LOCCness of the underlying evolution, thereby establishing the nonclassicality of the gravitational dynamics, which can no longer be explained by a local classical field. As a prominent application of this scheme we study systems of quantum harmonic oscillators initialized in coherent states following a normal distribution and interacting via Newtonian gravity, and discuss a possible physical implementation with torsion pendula. One of our main technical contributions is the analytical calculation of the above LOCC inequality for this family of systems. As opposed to existing tests based on the detection of gravitationally mediated entanglement, our proposal works with coherent states alone, and thus it does not require the generation of largely delocalized states of motion nor the detection of entanglement, which is never created at any point in the process. Published by the American Physical Society 2024
We establish limitations and bounds on the transmission of quantum states between gravitationally interacting mechanical oscillators under different models of gravity. This provides benchmarks that can enable tests for quantum features of gravity. Our proposal does not require the measurement of gravitationally induced entanglement and only requires final measurements of a single subsystem. We discuss bounds for classical models based on local operations and classical communication when considering coherent-state alphabets, and we discuss the transfer of quantum squeezing for falsifying the Schr\"odinger-Newton model.
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.
The question of whether gravity is fundamentally quantum remains one of the deepest open problems in modern physics. A recently explored approach consists of testing gravity's ability to entangle quantum systems, which requires preparing and controlling massive quantum states - a formidable experimental challenge. We propose an alternative strategy that circumvents the need for quantum state engineering. We show that, if gravity is classical, it must necessarily modify momentum statistics in a non-unitary way. We consider the corresponding linearized master equation for two harmonically trapped objects interacting gravitationally and establish a lower bound on the noise that any classical gravitational interaction must induce. We then outline an experimental protocol based on a high-precision torsion pendulum at millikelvin temperatures, showing that the predicted diffusion, if present, is in principle detectable with near-term technology. Our approach offers a novel route to testing the classical versus quantum nature of gravity without requiring macroscopic quantum superpositions or precise control of the system's quantum state, thereby significantly reducing the experimental complexity.
The prediction of nonlocal phenomena is a key attribute of quantum mechanics that distinguishes it from classical theories. It was recently suggested that state swapping is one such effect that a fundamentally classical gravitational field cannot give rise to. The reasoning was that the phenomenology of classical fields is restricted to local operations and classical communication (LOCC), whereas swapping is a non-LOCC effect, so gravity must not be a classical channel if it can give rise to such a phenomenon. Here, we show that the Hamiltonian of semiclassical gravity results in an evolution of coherent states that is virtually indistinguishable from swapping them, both theoretically and experimentally. Our results indicate that drawing a definitive conclusion about the nature of gravity based solely on its ability to swap a pair of coherent states would be premature. We discuss the implications of these results regarding proposed experimental tests for the quantum nature of gravity and clarify some conceptual issues.
Probing the quantum nature of gravity is one of the most profound open challenges in physics. A promising direction is the Gravitationally Induced Entanglement (GIE) protocol, where two initially unentangled probes become entangled solely through local interactions with a mediator of interaction, the gravitational field. Such entanglement would imply that gravity must carry quantum features, namely, it must possess at least a couple of incompatible observables. This thesis further expands the GIE protocol and its Theory-Independent argument by introducing a general, dynamics-independent inequality: the quantum correlation gain between the probes is upper-bounded by the non-commutativity of the mediator’s observables and its Hilbert space dimension. This bound holds for arbitrary interactions and any finite-dimensional systems. A decoherence analysis shows the bound vanishes when the mediator becomes classical. These results provide a quantitative, operational tool for observing the non-classicality of mediators, thereby expanding the conceptual and experimental reach of GIE-based tests of gravity.
The interplay between gravity and quantum mechanics remains a central open problem in modern physics. In this talk, I will discuss how a fundamentally classical, local gravitational interaction necessarily induces a diffusive modification of quantum dynamics. This diffusion leads to measurable noise even in the classical regime and provides a novel, experimentally accessible signature that does not require macroscopic quantum superpositions. I will derive a lower bound on the gravitational noise required to prevent entanglement generation and outline an experimental proposal based on torsion pendulums to test this bound. Next, I will consider the Schrödinger-Newton equation—a paradigmatic model of semiclassical gravity—which predicts nonlinear, self-induced gravitational effects. I will show how a periodic modulation of the trap frequency in levitated mechanical oscillators can amplify these otherwise negligible deviations by up to six orders of magnitude. The protocol remains feasible within current technologies and opens new pathways to experimentally test the SN dynamics through precise monitoring of the system’s position variance.