Bound on quantum scrambling with all-to-all interactions

Abstract

We prove bounds on operator growth and infinite temperature\nout-of-time-ordered correlators in many-body systems with $N$\nspin-$\\frac{1}{2}$ degrees of freedom which interact via two-body all-to-all\ninteractions. Our results parametrically improve previous bounds, and sharply\nconstrain when and how quantum simulators, including trapped ion crystals and\ncavity quantum electrodynamics, can study quantum gravity.\n