From Topological to Quantum Entanglement

TL;DR

This paper explores the relationship between topological theories and quantum entanglement, demonstrating how entangled states can be represented by cobordisms and calculating their von Neumann entropy.

Contribution

It introduces a formal mathematical framework linking topological quantum field theories to quantum entanglement representations.

Findings

Entangled states can be modeled by cobordisms of topological spaces.

Von Neumann entropy can be computed within this topological framework.

Topological interpretation of quantum correlations enhances understanding of entanglement.

Abstract

Entanglement is a special feature of the quantum world that reflects the existence of subtle, often non-local, correlations between local degrees of freedom. In topological theories such non-local correlations can be given a very intuitive interpretation: quantum entanglement of subsystems means that there are "strings" connecting them. More generally, an entangled state, or similarly, the density matrix of a mixed state, can be represented by cobordisms of topological spaces. Using a formal mathematical definition of TQFT we construct basic examples of entangled states and compute their von Neumann entropy.