Quantum entanglement of masses with nonlocal gravitational interaction
Ulrich K. Beckering Vinckers, Álvaro de la Cruz-Dombriz, Anupam Mazumdar
Abstract
We examine the quantum gravitational entanglement of two test masses in the context of linearized general relativity with specific nonlocal interaction with matter. To accomplish this, we consider an energy-momentum tensor describing two test particles of equal mass with each possessing some nonzero 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 nonlocality of the gravitational interaction results in a decrease in both of these quantities.