Entanglement of purification: from spin chains to holography

TL;DR

This paper investigates the entanglement of purification across different quantum systems, proposing conjectures supported by numerical and analytical results, and explores its implications for tensor networks and holographic geometry.

Contribution

It introduces conjectures for the entanglement of purification in spin chains, conformal field theories, and tensor networks, linking entanglement properties to holography and tensor network methods.

Findings

Conjectured values for entanglement of purification in various models.

Supported conjectures with numerical and analytical evidence.

Highlighted applications in tensor networks and holographic geometry.

Abstract

Purification is a powerful technique in quantum physics whereby a mixed quantum state is extended to a pure state on a larger system. This process is not unique, and in systems composed of many degrees of freedom, one natural purification is the one with minimal entanglement. Here we study the entropy of the minimally entangled purification, called the entanglement of purification, in three model systems: an Ising spin chain, conformal field theories holographically dual to Einstein gravity, and random stabilizer tensor networks. We conjecture values for the entanglement of purification in all these models, and we support our conjectures with a variety of numerical and analytical results. We find that such minimally entangled purifications have a number of applications, from enhancing entanglement-based tensor network methods for describing mixed states to elucidating novel aspects of the emergence of geometry from entanglement in the AdS/CFT correspondence.