A Robertson-type Uncertainty Principle and Quantum Fisher Information

Paolo Gibilisco, Daniele Imparato, Tommaso Isola

Let $A_1,...,A_N$ be complex selfadjoint matrices and let $\rho$ be a density matrix. The Robertson uncertainty principle $$ det (Cov_ρ(A_h,A_j)) \geq det (- \frac{i}{2} Tr (ρ[A_h,A_j…