Probing Scrambling Using Statistical Correlations between Randomized Measurements

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 it can be realized in state-of-the-art quantum simulation experiments.