Unitary $n$-designs via random quenches in atomic Hubbard and Spin models: Application to the measurement of R\'enyi entropies

TL;DR

This paper introduces a framework for generating approximate unitary $n$-designs using random quenches in atomic Hubbard and spin models, enabling efficient measurement of R\'enyi entropies with robustness against experimental imperfections.

Contribution

It generalizes previous protocols to a wider class of models and analyzes their performance considering decoherence and statistical errors.

Findings

The protocol efficiently produces approximate unitary $n$-designs.

Numerical and analytical studies show robustness against imperfections.

Connections to many-body quantum chaos are established.

Abstract

We present a general framework for the generation of random unitaries based on random quenches in atomic Hubbard and spin models, forming approximate unitary $n$-designs, and their application to the measurement of R\'enyi entropies. We generalize our protocol presented in [Elben2017: arXiv:1709.05060, to appear in Phys. Rev. Lett.] to a broad class of atomic and spin lattice models. We further present an in-depth numerical and analytical study of experimental imperfections, including the effect of decoherence and statistical errors, and discuss connections of our approach with many-body quantum chaos.