Testing the Quantumness of Gravity without Entanglement

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.

Popular Summary

Of the four fundamental forces, gravity is the most elusive when it comes to understanding its underlying character. The extreme weakness of the gravitational interaction, compared to those of the other forces, makes investigations into its true nature so far impossible to realize. In particular, it remains unclear whether gravity is ultimately a classical or quantum phenomenon. In this work, we propose a new type of experiment that may start to shed light on this fundamental question.

Previous proposals have focused on the detection of gravitationally mediated entanglement, the idea being that a classical gravitational field should not lead to entanglement between distant quantum systems. The problem with these proposals is that they are exceedingly difficult to realize, mainly because quantum entanglement is extremely fragile. We propose a completely different type of experiment: looking more closely at the whole dynamics induced by gravity on a quantum system. Using sophisticated mathematical techniques from quantum information theory, we develop tools to tell whether such dynamics may or may not have been induced by a classical gravitational field. Our tools work perfectly well also when no entanglement is ever generated at any point in the process.

We hope that our proposal will help design experiments that may answer this fundamental question about the nature of gravity earlier than expected.

Figure 1

(a) Quantum systems $A_1,\dots ,A_n$, initially prepared in a random pure state $\{p_{\alpha },{\psi }_{\alpha }{\}}_{\alpha }$, evolve with a coherent global isometry $U$. (b) The same systems undergo an evolution modeled by an LOCC. In both cases, at the end the value of $\alpha$ is revealed, and the system is subjected to the binary measurement $({\psi }_{\alpha }^{\prime },\mathbb{1}-{\psi }_{\alpha }^{\prime })$, where $|{\psi }_{\alpha }^{\prime }⟩≔U|{\psi }_{\alpha }⟩$.

Figure 2

A system of one-dimensional quantum harmonic oscillators. The various angles are defined in Eq. (60). Note that for the most general three-dimensional arrangement the two dashed lines will not intersect.

Figure 3

Two harmonic oscillators aligned.

Figure 4

The right-hand side of the LOCC inequality Eq. (95) plotted as a function of $\gamma t$ for several values of $\lambda$. Observe the approximately linear decrease with time of $f_{2,L}(0,t)$ for small times $t$, in line with the prediction of Theorem 12.

Figure 5

Four identical oscillators aligned.

Figure 6

Optomechanical torsion balance. Panel (a) shows a sketch of a torsion pendulum with a dumbbell-shaped body suspended from a thin wire with torsion constant $\tau$. A magnetic damper attached to the wire damps mechanical modes other than the torsional one [105]. Panel (b) presents a scheme of the optomechanical system composed of the torsion pendulum and two optical cavities. The light output of each cavity is a measure of the position of the corresponding edge of the pendulum. Independent measurements of the position of each end of the pendulum can be added or subtracted to discriminate between purely rotational motion and pendular swinging.

Figure 7

Gravitational interaction between two torsion balances. Two torsion pendula are placed with their equilibrium orientations (dashed lines) in parallel and let interact through gravity. An electromagnetic shield of thickness $d_{\mathrm{th}}$ is placed in between the two pendula to suppress electromagnetic interactions, EM shield. The minimum distance between the surface of any sphere and the EM shield is given by $d_s$. The rotational degrees of freedom of each pendulum are monitored through their coupling to two cavity fields (red lines).