Entanglement Structure of Non-Gaussian States and How to Measure It

TL;DR

This paper introduces a scalable protocol for characterizing the entanglement structure of complex quantum states using experimentally measured correlation functions, applicable to non-Gaussian states and relevant for studying quantum chaos.

Contribution

The authors develop a polynomial-scaling method to measure entanglement in non-Gaussian states by extending Gaussian parameterizations with higher-order correlations.

Findings

Protocol accurately predicts early time thermalization dynamics.

Method signals the onset of quantum chaos via entanglement Hamiltonian.

Applicable to current and future quantum simulation experiments.

Abstract

Rapidly growing capabilities of quantum simulators to probe quantum many-body phenomena require new methods to characterize increasingly complex states. We present a protocol that constrains quantum states by experimentally measured correlation functions which only scales polynomially with system size. This method enables measurement of a quantum state's entanglement structure, opening a new route to study entanglement-related phenomena. Our approach extends Gaussian state parameterizations by systematically incorporating higher-order correlations. We show the protocol's usefulness in conjunction with current and forthcoming experimental capabilities, focusing on weakly interacting fermions as a proof of concept. Here, the lowest non-trivial expansion quantitatively predicts early time thermalization dynamics, including signaling the on-set of quantum chaos indicated by the entanglement Hamiltonian.