Stabilizer entropy dynamics after a quantum quench

Stabilizer entropies (SE) measure deviations from stabilizer resources and as such are a fundamental ingredient for quantum advantage. In particular, the interplay of SE and entanglement is at the root of the complexity of classically simulating quantum many-body systems. In this paper, we study the dynamics of SE in a quantum many-body system away from the equilibrium after a quantum quench in an integrable system. We obtain two main results: (i) we show that SE, despite being an L-extensive quantity, equilibrates in a time that scales at most linearly with the subsystem size; and (ii) we show that there is a SE length increasing linearly in time, akin to correlations and entanglement spreading.