Classical Simulability from Operator Entanglement Scaling
The authors rigorously link Heisenberg operator entanglement to whether an operator can be efficiently represented by a matrix-product operator (MPO). They find that volume-law scaling of local-operator entanglement (LOE) Rényi entropies for $\alpha \geq 1$ prevents efficient MPO approximation for all states. Conversely, logarithmic scaling of $\alpha < 1$ entropies guarantees MPO simulability when considering specific classes of correlations like infinite temperature autocorrelation functions.