Probing entanglement entropy via randomized measurements

TL;DR

This paper introduces a new experimental protocol using randomized measurements to efficiently probe entanglement entropy in quantum systems, demonstrated on a trapped-ion simulator, revealing entanglement growth and system coherence.

Contribution

The paper presents a universal, experimentally feasible method for measuring entanglement entropy in large quantum systems using randomized measurements, advancing quantum characterization techniques.

Findings

Successfully measured entanglement growth in a quantum simulator

Demonstrated the protocol's effectiveness in both ordered and disordered systems

Proved the system's coherent dynamics through entropy measurements

Abstract

Entanglement is the key feature of many-body quantum systems, and the development of new tools to probe it in the laboratory is an outstanding challenge. Measuring the entropy of different partitions of a quantum system provides a way to probe its entanglement structure. Here, we present and experimentally demonstrate a new protocol for measuring entropy, based on statistical correlations between randomized measurements. Our experiments, carried out with a trapped-ion quantum simulator, prove the overall coherent character of the system dynamics and reveal the growth of entanglement between its parts - both in the absence and presence of disorder. Our protocol represents a universal tool for probing and characterizing engineered quantum systems in the laboratory, applicable to arbitrary quantum states of up to several tens of qubits.