A simpler inequality follows without a convex roof σ σ A 2 F Q [ ϱ ϱ , B ] ≥ ≥ | ⟨ ⟨ i [ A , B ] ⟩ ⟩ | 2 , which is stronger than the Heisenberg uncertainty relation, since for the quantum Fisher information we have F Q [ ϱ ϱ , B ] ≤ ≤ 4 σ σ B , while for pure states the equality holds.