Path-entangling evolution and quantum gravitational interaction

TL;DR

This paper investigates the conditions under which gravitational interactions can generate entanglement between spatially superposed masses, revealing that population-preserving CPTP maps can only create entanglement if they are inseparable.

Contribution

It establishes a fundamental link between population-preserving CPTP maps and their ability to generate entanglement, challenging certain models of gravitational interaction.

Findings

Population-preserving CPTP maps are inseparable if and only if they can create entanglement.

Models of gravity described by inseparable operations do not necessarily generate entanglement.

The results constrain the possible quantum evolution of superposed masses under gravity.

Abstract

We explore a general feature of the interaction mediated by the gravitational fields of spatially superposed masses. For this purpose, based on quantum information theory, we characterize the evolution of two particles each in a superposition state of paths. The evolution is assumed to be given by a completely positive trace-preserving (CPTP) map. We further assume that the probability of particle being on each path is unchanged during the evolution. This property is called population-preserving. We examine when a population-preserving CPTP map can create entanglement in terms of separable operations, which form a large class of local operations and classical communication (LOCC). In general, entanglement is not always generated by inseparable or non-LOCC operations, and one can consider a model of gravity described by an inseparable operation which does not create entanglement. However, we find that a population-preserving CPTP map is inseparable if and only if it can create entanglement. This means that the above model of gravity is incompatible with the possible evolution of spatially superposed masses.