Uncertainty Principle and Quantum Fisher Information - II

Abstract

Heisenberg and Schr{ö}dinger uncertainty principles give lower bounds for the product of variances $Va{r}_{\rho }(A)\cdot Va{r}_{\rho }(B)$, in a state $\rho$, if the observables $A,B$ are not compatible, namely if the commutator $[A,B]$ is not zero. In this paper we prove an uncertainty principle in Schr{ö}dinger form where the bound for the product of variances $Va{r}_{\rho }(A)\cdot Va{r}_{\rho }(B)$ depends on the area spanned by the commutators $[\rho ,A]$ and $[\rho ,B]$ with respect to an arbitrary quantum version of the Fisher information.

v2, Minor revision. v3, changes made to conform to version accepted on J. Math. Phys

Cited by in corpus (5)

• The quantum Chernoff bound as a measure of distinguishability between density matrices: application to qubit and Gaussian states
• Higher entropic uncertainty relations for anti-commuting observables
• Uncertainty principle with quantum Fisher information
• Inequalities for quantum skew information
• A volume inequality for quantum Fisher information and the uncertainty principle