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.
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.
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
In order to empirically test the quantum nature of gravity, it is essential to explore the construction of classical gravity theories that are as consistent with experiments as possible. In particular, the classical gravity field must receive input regarding matter distribution. Previously, such input has been constructed by taking expectation values of the matter density operator on the quantum state, or by using the outcomes of all measurements being performed on the quantum system---or by using information obtained by auxiliary observers (like those that lead to the continuous spontaneous localization and Diosi-Penrose collapses) that continuously monitor the quantum dynamics. We propose a framework that unifies these models, and argue that the Causal Conditional Formulation of Schr\"odinger-Newton (CCSN) theory, which takes classical inputs only from experimental and environmental channels---without auxiliary observers---is a minimum model within this framework. Since CCSN can be viewed as a quantum feedback control scheme, it can be made explicitly causal and free from pathologies that previously plagued Schr\"odinger-Newton theories. Since classical information from measurement results are used to generate classical gravity, CCSN can mimic quantum gravity better than one would naively expect for a classical theory---making it more subtle to perform tests of the quantum nature of gravity. We predict experimental signatures of CCSN in two concrete scenarios: (i) a single test mass continuously monitored by light, and (ii) two objects interacting via mutual gravity, each monitored separately. In case (i), we show that the mass-concentration effect of self classical gravity still makes CCSN much easier to test than testing the establishment of mutual entanglement, yet the signatures are more subtle than previously thought for classical gravity theories. Using time-delayed measurements and nonstationary measurements, which delay or suspend the flow of classical information into classical gravity, one can make CCSN more detectable. In case (ii), we show that mutual gravity generated by CCSN can lead to correlations that largely mimic signatures of quantum entanglement in steady-state measurements. Rigorous protocols that rule out local operation and classical communication channels, which are experimentally more challenging than simply testing steady-state entanglement, must be applied in order to completely rule out CCSN.
Finding a feasible scheme for testing the quantum mechanical nature of the gravitational interaction has been attracting an increasing level of attention. Gravity mediated entanglement generation so far appears to be the key ingredient for a potential experiment. In a recent proposal [D. Carney et al., PRX Quantum 2, 030330 (2021)] combining an atom interferometer with a low-frequency mechanical oscillator, a coherence revival test is proposed for verifying this entanglement generation. With measurements performed only on the atoms, this protocol bypasses the need for correlation measurements. Here, we explore formulations of such a protocol, and specifically find that in the envisioned regime of operation with high thermal excitation, semiclassical models, where there is no concept of entanglement, also give the same experimental signatures. We elucidate in a fully quantum mechanical calculation that entanglement is not the source of the revivals in the relevant parameter regime. We argue that, in its current form, the suggested test is only relevant if the oscillator is nearly in a pure quantum state, and in this regime the effects are too small to be measurable. We further discuss potential open ends. The results highlight the importance and subtleties of explicitly considering how the quantum case differs from the classical expectations when testing for the quantum mechanical nature of a physical system.
A promising route to testing quantum gravity in the laboratory is to look for gravitationally induced entanglement (GIE) between two or more quantum matter systems. To date, proposed tests have primarily focused on microsolid platforms prepared in highly nonclassical states, such as N00N states or strongly squeezed states. Here, we instead consider measuring GIE in atom interferometry as evidence of quantum gravity. We propose placing two atom interferometers next to each other in parallel and looking for correlations in the atom-number statistics at their output ports. Importantly, GIE is possible without challenging macroscopic superposition states, such as N00N or Schrödinger-cat states. Instead, GIE can arise using coherent, near-classical atomic states, substantially reducing the experimental complexity. Observing the effect in this regime would require the total mass of the atom interferometers to be near the Planck mass scale. However, we show that state-of-the-art quantum squeezing techniques in cold-atom systems can significantly lower this mass requirement, and outline realistic pathways by which the necessary mass scales could be achieved in the near future, placing laboratory tests of GIE with atom interferometers within reach.
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.
Can propagating gravitational waves serve as operational probes of the quantum nature of gravity? We address this question by developing a unified theoretical framework that combines spacetime geometry, quantum information, and gravitational-wave physics. Starting from the geodesic deviation equation in linearized General Relativity, we derive the effective detector Hamiltonian directly from spacetime geometry and construct the complete quantum dynamics for detector subsystems interacting with both classical and quantized propagating gravitational-wave fields. This unified formulation enables a direct comparison between classical and quantum descriptions of gravitational radiation within the same physical framework. We demonstrate that classical gravitational-wave backgrounds can induce mixedness in the detector state but cannot generate genuine quantum correlations between the detector subsystems. In contrast, quantized gravitational waves coherently mediate gravity-induced entanglement, quantum coherence, quantum memory, and nonclassical correlations, providing clear operational signatures of the quantum nature of propagating gravitational radiation. We further discuss how mesoscopic quantum mechanical oscillators offer a promising route towards experimentally probing these effects. Our results establish a geometric and quantum-information-based framework for exploring quantum gravity through propagating gravitational waves.