Bound on quantum scrambling with all-to-all interactions

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