Probing scrambling using statistical correlations between randomized measurements

Abstract

We propose and analyze a protocol to study quantum information scrambling using statistical correlations between measurements, which are performed after evolving a quantum system from randomized initial states. We prove that the resulting correlations precisely capture the so-called out-of-time-ordered correlators and can be used to probe chaos in strongly-interacting, many-body systems. Our protocol requires neither reversing time evolution nor auxiliary degrees of freedom, and can be realized in state-of-the-art quantum simulation experiments.

This version v2 (8 pages, 7 figures) includes important new results compared to our original submission. (1) We present a protocol and corresponding mathematical proof to access OTOCs with local operations, and which can be realized in quantum simulation experiments with available technology. (2) We illustrate the realization of the protocols with different examples for Hubbard and spin models