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Absence of gravitationally induced entanglement in certain semi-classical theories of gravity

Ward Struyve

TL;DR

The work investigates whether gravity can produce entanglement between massive quantum systems within semi-classical models where gravity is a classical potential in the Schrödinger equation. It shows that additively separable potentials (including NS, NSB, and Döner–Großardt’s V_R) do not generate entanglement, while the standard Newtonian potential can, highlighting a fundamental distinction between these models. By mapping to a BMV-style experiment and using an entanglement witness, the authors provide explicit time-dependent predictions: NS and NSB remain non-entangled, whereas Newtonian gravity yields entanglement under appropriate conditions, suggesting a path to experimental discrimination. Overall, the paper clarifies the limitations of semi-classical gravity in producing gravitationally induced entanglement and informs interpretation of tabletop tests probing the quantum nature of gravity.

Abstract

Bose et al. and Marletto and Vedral proposed an experiment to test whether gravity can induce entanglement between massive systems, arguing that the capacity to do so would imply the quantum nature of gravity. In this work, a class of semi-classical models is examined that treat gravity classically, through some potential in the Schrödinger equation, and it is shown that these models do not generate entanglement. This class includes the Newton-Schrödinger model, where gravity is sourced by the wave function, the Bohmian analogue, where gravity is sourced by actual point-particles, and an interpolating model proposed by Döner and Grossardt. These models are analyzed in the context of the proposed experiment and contrasted with the standard Newtonian potential, which does generate entanglement.

Absence of gravitationally induced entanglement in certain semi-classical theories of gravity

TL;DR

The work investigates whether gravity can produce entanglement between massive quantum systems within semi-classical models where gravity is a classical potential in the Schrödinger equation. It shows that additively separable potentials (including NS, NSB, and Döner–Großardt’s V_R) do not generate entanglement, while the standard Newtonian potential can, highlighting a fundamental distinction between these models. By mapping to a BMV-style experiment and using an entanglement witness, the authors provide explicit time-dependent predictions: NS and NSB remain non-entangled, whereas Newtonian gravity yields entanglement under appropriate conditions, suggesting a path to experimental discrimination. Overall, the paper clarifies the limitations of semi-classical gravity in producing gravitationally induced entanglement and informs interpretation of tabletop tests probing the quantum nature of gravity.

Abstract

Bose et al. and Marletto and Vedral proposed an experiment to test whether gravity can induce entanglement between massive systems, arguing that the capacity to do so would imply the quantum nature of gravity. In this work, a class of semi-classical models is examined that treat gravity classically, through some potential in the Schrödinger equation, and it is shown that these models do not generate entanglement. This class includes the Newton-Schrödinger model, where gravity is sourced by the wave function, the Bohmian analogue, where gravity is sourced by actual point-particles, and an interpolating model proposed by Döner and Grossardt. These models are analyzed in the context of the proposed experiment and contrasted with the standard Newtonian potential, which does generate entanglement.
Paper Structure (4 sections, 41 equations, 1 figure)

This paper contains 4 sections, 41 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Absence of entanglement generation
  3. Experimental setup
  4. Acknowledgments

Figures (1)

  • Figure 1: Entanglement witness $W$ evaluated for the different potentials $V_{\textrm{N}}$, ${\widetilde{V}}_{\textrm{NS}}$ and ${\widetilde{V}}_{\textrm{NSB}}$, plotted as a function of time. Negativity of the witness indicates entanglement.