Classical Simulability from Operator Entanglement Scaling

• URL: http://arxiv.org/abs/2603.05656v1
• Date: Thu, 05 Mar 2026 20:18:05 GMT
• Title: Classical Simulability from Operator Entanglement Scaling
• Abstract summary: Local-operator entanglement (LOE) quantifies the nonlocal structure of Heisenberg operators and serves as a diagnostic of many-body chaos.<n>We provide rigorous bounds showing when an operator can be well-approximated by a matrix-product operator (MPO), given scaling of its LOE $$-Rényi entropies.<n>Our results put on firm footing the expectation that a low operator entanglement implies efficient tensor network representability.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $α$-Rényi entropies. Specifically, we prove that a volume law scaling for $α\geq 1$ implies that the operator cannot be approximated efficiently as an MPO while faithfully reproducing all expectation values. On the other hand, if we restrict to correlations over a relevant sub-class of (ensembles of) states, then logarithmic scaling of the $α< 1$ Rényi LOE entropies implies MPO simulability. This result covers a range of relevant quantities, including infinite temperature autocorrelation functions, out-of-time-ordered correlators, and average-case expectation values over ensembles of computational basis states. Beyond this regime, we provide numerical evidence together with a random matrix model to argue that, also for out-of-equilibrium expectation values, logarithmic scaling for $α< 1$ Rényi LOE typically guarantees simulability. Our results put on firm footing the heuristic expectation that a low operator entanglement implies efficient tensor network representability, extending celebrated foundational results from the theory of matrix-product states and providing a formal link between quantum chaos and classical simulability.

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