Quantum Fisher Information as the Speed Limit for Multipartite Entanglement
We derive a universal upper bound on the speed of multipartite entanglement generation. For arbitrary differentiable pure multipartite states undergoing parameter-dependent evolution, we prove that the rate of change of generalized concurrence is bounded by the square root of the quantum Fisher information (QFI). The proof follows directly from the symmetric logarithmic derivative formalism, revealing the bound as a consequence of quantum estimation theory, while a complementary Schmidt-spectrum analysis identifies the conditions for saturation and yields a tighter bound for rank-two bipartitions. We illustrate these results in interacting many-body spin models and investigate their behavior across the quantum phase transition of the transverse-field Ising model. At the critical point, we find that the QFI can be strongly enhanced while the generalized concurrence is nearly stationary and its sensitivity to the coupling is suppressed. This demonstrates that the enhanced parameter sensitivity associated with quantum criticality need not arise from rapid changes in the magnitude of multipartite entanglement.