Classical Simulability from Operator Entanglement Scaling (opens in new tab)

arXiv:2603.05656v1 Announce Type: new Abstract: Local-operator entanglement (LOE) quantifies the nonlocal structure of Heisenberg operators and serves as a diagnostic of many-body chaos. We provide rigorous bounds showing when an operator can be well-approximated by a matrix-product operator (MPO), given asymptotic scaling of its LOE $\alpha$-R\'enyi entropies. Specifically, we prove that a volume law scaling for $\alpha\geq 1$ implies that the operator cannot be approximated efficiently as ...