Today's Experiments Suffice to Indirectly Verify the Quantum Essence of Gravity

TL;DR

This work argues that gravity-mediated entanglement (GME) can be indirectly established with today’s matter-wave interferometers by combining a direct test of the single-delocalized Schrödinger dynamics in a gravitational field with two plausible physical assumptions. It develops a CP time-evolution framework $\Phi_t$ and uses Choi matrices and semidefinite programming to connect a single-particle Schrödinger verification to entanglement generation between two delocalized masses. Under the mass-product assumption, numerical SDP demonstrates that current phase sensitivity could certify GME (bound $\lambda_0 \approx 0.9995$) for realistic masses and geometries, suggesting gravity’s quantum nature could be probed sooner than direct two-mass demonstrations. The results emphasize a theoretical bottleneck in connecting GME with gravity's foundational implications and motivate further work on relaxing assumptions and integrating with relativistic quantum frameworks.

Abstract

The gravity-mediated entanglement experiments employ concepts from quantum information to argue that if entanglement due to gravitational interaction is observed, then gravity cannot be described by a classical system. However, the proposed experiments remain beyond out current technological capability, with optimistic projections placing the experiment outside of short-term future. Here we argue that current matter-wave interferometers are sufficient to indirectly prove that gravitational interaction creates entanglement between two systems. Specifically, we prove that if we experimentally verify the Schrödinger equation for a single delocalized system interacting gravitationally with an external mass, then, under one of two reasonable assumptions, the time evolution of two delocalized systems will lead to gravity-mediated entanglement.

Figures (3)

• Figure 1: The spacetime diagram depicting two mass interferometers (blue and red) separated by a distance $d = \,\mathrm{450 \mu{}m}$, the values are based on bose2017spin. From time $t=0$ to time $t=1 \,\mathrm{s}$ magnetic field or laser pulses are used to coherently split the momentum of both particles, thus yielding two arms, $|L\rangle$ and $|R\rangle$, of the respective interferometers separated by the distance $\Delta x = \,\mathrm{250 \mu{}m}$. Then the arms are kept at constant separations and their gravitational interaction will (according to the Schrödinger equation) cause relative phaseshifts between the four combinations of the arms, entangling the two systems. The experiment concludes by applying the interferometric sequence in reverse, recombining the arms, and enabling to observe the gravity-mediated entanglement (GME).
• Figure 2: The spacetime diagram depicting a mass interferometer (blue) and macroscopic test masses $M_1$ and $M_2 = 2 M_1$ (red) at distances $d_1 = 55 \,\mathrm{mm}$ and $d_2 \approx \,\mathrm{78 \,\mathrm{mm}}$ from the center of mass of the interferometer, the values are based on plavala2025probing. From time $t = 0$ to $t = 1 \,\mathrm{s}$ magnetic field or laser pulses are used to coherently split the momentum of the particle, thus yielding two arms, $|L\rangle$ and $|R\rangle$, separated by $\Delta x = 10 \,\mathrm{cm}$. Then the arms are kept at constant separation. The external masses are positioned so that the phase shift due to the classical limit vanishes and thus any effects will be only due to quantum effects of gravity. The experiment concludes by applying the interferometric sequence in reverse and measuring the quantum effects of gravity.
• Figure 3: The plot of the smallest eigenvalue of the partial transpose of the final state of the GME experiment $\Phi_t(| + \rangle \! \langle + | \otimes | + \rangle \! \langle + |)$ as a function of the decoherence upper bound $\lambda_0$. If the smallest eigenvalue is negative, then the final state of the GME experiment $\Phi_t(| + \rangle \! \langle + | \otimes | + \rangle \! \langle + |)$ is entangled for all possible time evolutions $\Phi_t$ corresponding to the given value of $\lambda_0$. The red line is for completely positive time evolution $\Phi_t$, the blue, green, and yellow lines are outer approximations of positive time evolution $\Phi_t$ by enforcing positivity on $1000$, $100$, and $10$ randomly generated pure states.

Theorems & Definitions (4)

• Theorem 1
• proof
• Theorem 2
• proof