Quantum entanglement of masses with non-local gravitational interaction

TL;DR

This paper investigates how non-local gravitational interactions influence quantum entanglement between two masses, revealing that increased non-locality reduces entanglement measures like concurrence and entropy.

Contribution

It introduces a framework for analyzing quantum gravitational entanglement with non-local interactions within linearized General Relativity, including finite energy shifts and entanglement effects.

Findings

Non-local gravitational interactions lead to finite energy shifts.

Increased non-locality decreases quantum entanglement measures.

Two scenarios demonstrate the impact of non-locality on entanglement.

Abstract

We examine the quantum gravitational entanglement of two test masses in the context of linearized General Relativity with specific non-local interaction with matter. To accomplish this, we consider an energy-momentum tensor describing two test particles of equal mass with each possessing some non-zero momentum. After discussing the quantization of the linearized theory, we compute the gravitational energy shift which is operator-valued in this case. As compared to the local gravitational interaction, we find that the change in the gravitational energy due to the self-interaction terms is finite. We then move on to study the quantum gravity induced entanglement of masses for two different scenarios. The first scenario involves treating the two test masses as harmonic oscillators with an interaction Hamiltonian given by the aforesaid gravitational energy shift. In the second scenario, each of the test masses is placed in a quantum spatial superposition of two locations, based on their respective spin states, and their entanglement being induced by the gravitational interaction and the shift in the vacuum energy. For these two scenarios, we compute both the concurrence and the von Neumann entropy; showing that an increase in the non-locality of the gravitational interaction results in a decrease in both of these quantities.