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Can Newtonian Gravity Produce Quantum Entanglement?

Feng-Li Lin, Sayid Mondal

TL;DR

Can Newtonian gravity generate entanglement between mesoscopic quantum bodies? The paper tests this by comparing three gravity-matter models—mini-superspace quantum gravity, semiclassical gravity, and stochastic gravity—against the gravitationally induced entanglement (GIE) protocol. It finds entanglement arises only in the mini-superspace scenario, where the parity of the gravitational tidal field is quantized, while semiclassical and stochastic models yield only product states; it also shows that perturbative truncations can falsely suggest entanglement. These results support the view that classical gravity cannot mediate entanglement at low energies and highlight the need for careful, higher-order analyses in gravity-matter interactions for experimental tests of quantum gravity.

Abstract

We investigate whether Newtonian gravity can generate quantum entanglement between mesoscopic quantum bodies modeled as superposed mass quadrupoles using three complementary approaches: mini-superspace, semiclassical gravity, and stochastic gravity. We systematically analyze gravitationally induced entanglement (GIE) mechanisms and the conditions under which they can arise. Our results support the GIE hypothesis by showing that the mini-superspace framework, which quantizes the parity of the gravitational tidal field, can entangle spatially separate quantum bodies. In contrast, the semiclassical and stochastic gravity models, in which the tidal gravitational field sourced by the quantum bodies remains classical, fail to entangle the final state. These findings clarify recent claims that classical gravity might induce entanglement, and reveal how perturbative treatments can lead to misleading conclusions.

Can Newtonian Gravity Produce Quantum Entanglement?

TL;DR

Can Newtonian gravity generate entanglement between mesoscopic quantum bodies? The paper tests this by comparing three gravity-matter models—mini-superspace quantum gravity, semiclassical gravity, and stochastic gravity—against the gravitationally induced entanglement (GIE) protocol. It finds entanglement arises only in the mini-superspace scenario, where the parity of the gravitational tidal field is quantized, while semiclassical and stochastic models yield only product states; it also shows that perturbative truncations can falsely suggest entanglement. These results support the view that classical gravity cannot mediate entanglement at low energies and highlight the need for careful, higher-order analyses in gravity-matter interactions for experimental tests of quantum gravity.

Abstract

We investigate whether Newtonian gravity can generate quantum entanglement between mesoscopic quantum bodies modeled as superposed mass quadrupoles using three complementary approaches: mini-superspace, semiclassical gravity, and stochastic gravity. We systematically analyze gravitationally induced entanglement (GIE) mechanisms and the conditions under which they can arise. Our results support the GIE hypothesis by showing that the mini-superspace framework, which quantizes the parity of the gravitational tidal field, can entangle spatially separate quantum bodies. In contrast, the semiclassical and stochastic gravity models, in which the tidal gravitational field sourced by the quantum bodies remains classical, fail to entangle the final state. These findings clarify recent claims that classical gravity might induce entanglement, and reveal how perturbative treatments can lead to misleading conclusions.

Paper Structure

This paper contains 12 sections, 29 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Preparation of mesoscopic quantum bodies
  3. Newtonian Gravity of Quantum Bodies
  4. Mini-superspace approach
  5. Semi-classical gravity approach
  6. Stochastic gravity approach
  7. Does Newtonian gravity entangle quantum bodies?
  8. Entanglement production in mini-superspace approach
  9. No entanglement production in semiclassical and stochastic gravity approaches
  10. Confusing GIE-violating result due to perturbative calculations
  11. Discussion and conclusion
  12. Acknowledgements

Figures (1)

  • Figure 1: (a) Quantum body of mass quadrupole with its sign in the equal-weight superposed state. The $\pm \delta m$ are the local mass contrasts of either sign with respect to the underlying uniform mass distribution. (b) Two such quantum bodies with mass quadrupoles interact via the tidal gravitational fields. The main characteristics of this interaction are dictated by Newtonian gravity; however, its quantum nature will be scenario dependent.