Statistical correlations between locally randomized measurements: a toolbox for probing entanglement in many-body quantum states

Understand

We develop a general theoretical framework for measurement protocols employing statistical correlations of randomized measurements.

• We focus on locally randomized measurements implemented with local random unitaries in quantum lattice models.
• In particular, we discuss the theoretical details underlying the recent measurement of the second R\'{e}nyi entropy of highly mixed quantum states consisting of up to $10$ qubits in a trapped-ion quantum simulator [Brydges et al., Science 364, 260 (2019)].
• We generalize the protocol to access the overlap of quantum states, prepared sequentially in an experiment.