OTOCs and topological invariants from statistical correlations of randomized measurements
Recently, statistical correlations of randomized measurements have emerged as a new tool to probe properties of many-body quantum states beyond standard observables. Here, I focus on locally randomized measurements in spin models, implemented by the application of local random unitaries and a subsequent measurement in a fixed basis. I will discuss two applications: First, I'll present a protocol to measure out-of-time ordered correlation functions (OTOCs), without the necessity of implementing time reversed operations or ancilla degrees of freedom. Secondly, I'll show how the same tools can be used to access topological invariants of symmetry protected topological phases in one-dimensional spin systems. Concentrating on invariants arising from inversion and time-reversal symmetry, which cannot be accessed using traditional string order parameters, I'll discuss measurement protocols, and present examples in the context of the SHH model.
Host: Mohammad Hafezi