Role of matter coherence in entanglement due to gravity

TL;DR

This paper explores how the coherence of quantum objects influences gravitationally induced entanglement, proposing a witness to detect quantum gravity effects even without entanglement formation.

Contribution

It introduces an entangling-map witness based on coherence to test the quantum nature of gravity, applicable even when no entanglement is observed.

Findings

The witness can detect quantum gravity effects without entanglement.

Coherence of objects always contributes to the entangling map due to gravity.

The approach discusses decoherence effects and experimental implications.

Abstract

We investigate the quantum nature of gravity in terms of the coherence of quantum objects. As a basic setting, we consider two gravitating objects each in a superposition state of two paths. The evolution of objects is described by the completely positive and trace-preserving (CPTP) map with a population-preserving property. This property reflects that the probability of objects being on each path is preserved. We use the $\ell_1$-norm of coherence to quantify the coherence of objects. In the present paper, the quantum nature of gravity is characterized by an entangling map, which is a CPTP map with the capacity to create entanglement. We introduce the entangling-map witness as an observable to test whether a given map is entangling. We show that, whenever the gravitating objects initially have a finite amount of the $\ell_1$-norm of coherence, the witness tests the entangling map due to gravity. Interestingly, we find that the witness can test such a quantum nature of gravity, even when the objects do not get entangled. This means that the coherence of gravitating objects always becomes the source of the entangling map due to gravity. We further discuss a decoherence effect and an experimental perspective in the present approach.