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.
@article{arxiv.1806.05747,
title = {Probing entanglement entropy via randomized measurements},
author = {Tiff Brydges and Andreas Elben and Petar Jurcevic and Benoît Vermersch and Christine Maier and Ben P. Lanyon and Peter Zoller and Rainer Blatt and Christian F. Roos},
journal= {arXiv preprint arXiv:1806.05747},
year = {2019}
}