Towards measuring Entanglement Entropies in Many Body Systems

TL;DR

This paper investigates how the entanglement entropy in quantum many-body systems can be inferred from the probability distributions of certain observables, providing methods to measure or bound the entropy in various models.

Contribution

It establishes a connection between entanglement entropy and observable distributions, offering practical approaches to measure entanglement in complex quantum systems.

Findings

Shannon entropy of symmetry observables bounds entanglement entropy.

In some models, the bound is tight and directly yields the entropy.

Examples include BEC wave functions, Dicke model, XY spin chain, and disordered chains.

Abstract

We explore the relation between entanglement entropy of quantum many body systems and the distribution of corresponding, properly selected, observables. Such a relation is necessary to actually measure the entanglement entropy. We show that in general, the Shannon entropy of the probability distribution of certain symmetry observables gives a lower bound to the entropy. In some cases this bound is saturated and directly gives the entropy. We also show other cases in which the probability distribution contains enough information to extract the entropy: we show how this is done in several examples including BEC wave functions, the Dicke model, XY spin chain and chains with strong randomness.