Mixed-State Entanglement from Local Randomized Measurements
Andreas Elben, Richard Kueng, Hsin-Yuan Huang, Rick van Bijnen, Christian Kokail, Marcello Dalmonte, Pasquale Calabrese, Barbara Kraus, John Preskill, P. Zoller, Benoît Vermersch
Abstract
We propose a method for detecting bipartite entanglement in a many-body mixed state based on estimating moments of the partially transposed density matrix. The estimates are obtained by performing local random measurements on the state, followed by postprocessing using the classical shadows framework. Our method can be applied to any quantum system with single-qubit control. We provide a detailed analysis of the required number of experimental runs, and demonstrate the protocol using existing experimental data [Brydges et al., Science 364, 260 (2019)SCIEAS0036-807510.1126/science.aau4963].