# Entanglement, space-time and the Mayer-Vietoris theorem

## TL;DR

This paper explores the connection between quantum entanglement and space-time topology, proposing a novel interpretation of algebraic topological tools as quantum information processes to support the ER-EPR duality in quantum gravity.

## Contribution

It introduces a new perspective linking the Mayer-Vietoris theorem to quantum entanglement, providing a potential step towards proving the ER-EPR duality.

## Key findings

- Reinterpreted Mayer-Vietoris morphisms as quantum entangler gates
- Linked algebraic topology to quantum information theory
- Suggested a topological basis for quantum gravity principles

## Abstract

Entanglement appears to be a fundamental building block of quantum gravity leading to new principles underlying the nature of quantum space-time. One such principle is the ER-EPR duality. While supported by our present intuition, a proof is far from obvious. In this article I present a first step towards such a proof, originating in what is known to algebraic topologists as the Mayer-Vietoris theorem. The main result of this work is the re-interpretation of the various morphisms arising when the Mayer-Vietoris theorem is used to assemble a torus-like topology from more basic subspaces on the torus in terms of quantum information theory resulting in a quantum entangler gate (Hadamard and c-NOT).