Mechanism for the quantum natured gravitons to entangle masses

TL;DR

This paper explores how the quantum nature of gravitons can induce entanglement between two masses in harmonic traps, emphasizing the necessity of quantum gravity for such entanglement and analyzing different dynamical scenarios.

Contribution

It demonstrates that quantum gravitons can entangle matter systems and distinguishes this from classical gravity, using perturbation theory and specific oscillator models.

Findings

Quantum gravitons induce entanglement between masses.

Classical gravity does not produce such entanglement.

The spin-2 nature of gravitons is crucial for entanglement.

Abstract

This paper points out the importance of the quantum nature of the gravitational interaction with matter in a linearized theory of quantum gravity induced entanglement of masses (QGEM). We will show how the quantum interaction entangles the steady states of a closed system (eigenstates) of two test masses placed in the harmonic traps, and how such a quantum matter-matter interaction emerges from an underlying quantum gravitational field. We will rely upon quantum perturbation theory highlighting the critical assumptions for generating a quantum matter-matter interaction and showing that a classical gravitational field does not render such an entanglement. We will consider two distinct examples; one where the two harmonic oscillators are static and the other where the harmonic oscillators are non-static. In both the cases it is the quantum nature of the gravitons interacting with the harmonic oscillators that are responsible for creating an entangled state with the ground and the excited states of harmonic oscillators as the Schmidt basis. We will compute the concurrence as a criterion for the above entanglement and highlight the role of the spin-2 nature of the graviton for entangling the two harmonic oscillators.