Quantifying multiparticle entanglement with randomized measurements

TL;DR

This paper introduces a method using randomized measurements to quantify multiparticle entanglement, providing a statistical framework and demonstrating its effectiveness on various quantum states, including noisy circuits.

Contribution

It develops a novel approach to measure multiparticle entanglement via randomized measurements and analyzes the measurement resources needed for accurate estimation.

Findings

Effective quantification of multiparticle concurrence using randomized measurements.

Numerical validation on typical entangled states and random quantum circuits.

Applicability to noisy quantum circuits with depolarization errors.

Abstract

Randomized measurements constitute a simple measurement primitive that exploits the information encoded in the outcome statistics of samples of local quantum measurements defined through randomly selected bases. In this work we exploit the potential of randomized measurements in order to probe the amount of entanglement contained in multiparticle quantum systems as quantified by the multiparticle concurrence. We further present a detailed statistical analysis of the underlying measurement resources required for a confident estimation of the introduced quantifiers using analytical tools from the theory of random matrices. The introduced framework is demonstrated by a series of numerical experiments analyzing the concurrence of typical multiparticle entangled states as well as of ensembles of output states produced by random quantum circuits. Finally, we examine the multiparticle entanglement of mixed states produced by noisy quantum circuits consisting of single- and two-qubit gates with non-vanishing depolarization errors, thus showing that our framework is directly applicable in the noisy intermediate-scale regime.