Gravitational quantum switch on a superposition of spherical shells

TL;DR

This paper proposes a model for a gravitational quantum switch using superpositions of spherical shell geometries, demonstrating how quantum operations can be entangled with gravitational states in a semi-classical framework.

Contribution

It introduces a protocol for implementing a gravitational quantum switch with superposed geometries produced by spherical shells, highlighting novel features like nonisometric superpositions and free-falling agents.

Findings

Protocol for gravitational quantum switch formulated

Superposition of geometries with identical exterior and differing interior

Agent in free fall entangled with geometry, preventing global information access

Abstract

In the absence of a complete theory of quantum gravity, phenomenological models built upon minimal assumptions have been explored for the analysis of possible quantum effects in gravitational systems. Implications of a superposition of geometries have been considered in such models, including the occurrence of processes with indefinite order. In a gravitational quantum switch, in particular, the order of operations applied by two agents on a target system is entangled with the state of the geometry. We consider a model describing the superposition of geometries produced by distinct arrangements of spherical mass shells, and show that a protocol for the implementation of a gravitational quantum switch can be formulated in such a system. The geometries in superposition are identical in an exterior region outside a given radius, and differ within such a radius. The exterior region provides a classical frame from which the superposition of geometries in the interior region can be probed. One of the agents crosses the interior region and becomes entangled with the geometry, which is explored as a resource for the implementation of the quantum switch. Novel features of the protocol include the superposition of nonisometric geometries, the existence of a region with a definite geometry, and the fact that the agent that experiences the superposition of geometries is in free fall, preventing information on the global geometry to be obtained from within its laboratory.