Quantifying multiparticle entanglement with randomized measurements

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.