Theory Seminar: Probing many-body quantum states with randomized measurements

Andreas Elben (Universität Innsbruck)
Randomized measurements are a technique to probe many-body quantum states beyond familiar, low-order observables.

Andreas Elben (Universität Innsbruck)
Herbert-Walther Lecture Hall G0.25
Wed, 12. February 2020, 11:30 am

Abstract:

Randomized measurements are a technique to probe many-body quantum states beyond familiar, low-order observables. In this talk, I introduce the technique using the example of measuring the second-order Rényi entropy in a trapped ion quantum simulator. Subsequently, I focus on two applications: First, I will present a scheme to measure (mixed-state) fidelities of two quantum states prepared on two, potentially very different, quantum devices. Importantly, the protocol requires only local measurements in randomized product bases and classical communication between the two devices. Second, I present protocols to access topological invariants for symmetry protected topological (SPT) phases, being quantized, nonlocal correlators of the many-body wavefunction. For one-dimensional spin systems, I show explicitly how to measure SPT invariants arising from inversion, time-reversal and unitary onsite symmetries. I illustrate the technique and its application in the context of the extended bosonic SSH model, as realized with Rydberg tweezer arrays.