Information-theoretical analysis of topological entanglement entropy and multipartite correlations

TL;DR

This paper explores the relationship between topological entanglement entropy and irreducible correlation in topologically ordered phases, establishing their equivalence under certain conditions and linking them to secret sharing protocols.

Contribution

It demonstrates the equivalence of topological entanglement entropy and irreducible correlation for states with an area law and zero correlation length, providing an information-theoretical interpretation.

Findings

Topological entanglement entropy and irreducible correlation coincide under specific conditions.

These measures are operationally equivalent to secret sharing protocol rates.

The work offers an information-theoretical perspective on multipartite correlations in topological phases.

Abstract

A special feature of the ground state in a topologically ordered phase is the existence of large scale correlations depending only on the topology of the regions. These correlations can be detected by the topological entanglement entropy or by a measure called irreducible correlation. We show that these two measures coincide for states obeying an area law and having zero-correlation length. Moreover, we provide an operational meaning for these measures by proving its equivalence to the optimal rate of a particular class of secret sharing protocols. This establishes an information-theoretical approach to multipartite correlations in topologically ordered systems.