# On a new relation between entanglement and geometry from M(atrix) theory

## TL;DR

This paper introduces a novel approach within M(atrix) theory to relate quantum entanglement between a probe and a source mass to gravitational potential energy and local geometric properties, linking quantum information to spacetime geometry.

## Contribution

It establishes a new connection between entanglement entropy and derivatives of gravitational potential, and proposes a scheme to relate entropy to local Riemann curvature in M(atrix) theory.

## Key findings

- Entanglement entropy is related to gravitational potential energy.
- Von Neumann entropy depends on derivatives of the gravitational potential.
- A conjectured relation links entropy to local Riemann curvature.

## Abstract

In the context of Matrix/light-cone gauge M-theory, we develop a new approach for computing quantum entanglement between a probe gravitating in the vicinity of a source mass and the source mass. We demonstrate that this entanglement is related to the gravitational potential energy between the two objects. We then show that the Von Neumann entropy is a function of two derivatives of the gravitational potential. We conjecture a relation between the entropy and the local Riemann tensor sampled by the probe, establishing a general scheme to relate entropy to local geometric data. This relation connects the rate of change, rotation, and twist of a small volume element at the probe's location to the quantum entanglement of the probe with the source.