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

By Andreas Elben, B. Vermersch, C. F. Roos, Peter Zoller. Physical Review A, 2018

152 citations recorded by the source corpus.

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. Furthermore, we discuss proposals for quantum state tomography based on randomized measurements within our framework and the respective scaling of statistical errors with system size.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/6c6d6d7ad6d2f824291aa09f205febd4c1a70c4f

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In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

Citations in the corpus

The randomized measurement toolbox (2022, background): “Asymptotic scalings M ∝ 2 w / ε 2 have been rigorously shown for equation (4) 24,36 and also observed for equation (3) 23,35,44 .”