ER=EPR, Entanglement Topology and Tensor Networks

TL;DR

This paper explores the relationship between quantum entanglement and topological connectivity through tensor networks, proposing a construction that links entanglement with topological structures in spacetime.

Contribution

It introduces a method to construct topological spaces from tensor networks and background spaces, illustrating the connection between entanglement and topology.

Findings

Entanglement corresponds to topological connectivity.

Tensor networks can be used to model spacetime topology.

The construction demonstrates the ER=EPR hypothesis.

Abstract

This paper discusses ER = EPR, the hypothesis of Susskind and Maldacena that entangled black holes are connected by an Einstein-Rosen bridge, and that more generally, quantum entanglement is accompanied by topological connectivity. Given a background space and a quantum tensor network, we describe how to construct a new topological space, that welds the network and the background space together. This construction embodies the principle that quantum entanglement and topological connectivity are intimately related.