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• W2950900311 abstract "Let $A_1,...,A_N$ be complex selfadjoint matrices and let $rho$ be a density matrix. The Robertson uncertainty principle $$ det (Cov_rho(A_h,A_j)) geq det (- frac{i}{2} Tr (rho [A_h,A_j])) $$ gives a bound for the quantum generalized covariance in terms of the commutators $ [A_h,A_j]$. The right side matrix is antisymmetric and therefore the bound is trivial (equal to zero) in the odd case $N=2m+1$. Let $f$ be an arbitrary normalized symmetric operator monotone function and let $ _{rho,f}$ be the associated quantum Fisher information. In this paper we prove the inequality $$ det (Cov_rho (A_h,A_j)) geq det (frac{f(0)}{2} _{rho,f}) $$ that gives a non-trivial bound for any $N in {mathbb N}$ using the commutators $[rho,A_h]$." @default.
• W2950900311 created "2019-06-27" @default.
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• W2950900311 date "2007-07-09" @default.
• W2950900311 modified "2023-09-27" @default.
• W2950900311 title "A Robertson-type Uncertainty Principle and Quantum Fisher Information" @default.
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