Uncertainty Principle and Quantum Fisher Information - II

Details Uncertainty Principle and Quantum Fisher Information - II Uncertainty Principle and Quantum Fisher Information - II

2007-01-24

arxiv.org/abs/math-ph/0701062v3

Physics

Mathematical Physics

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

Scientific paper

10.1063/1.2748210

Heisenberg and Schr{\"o}dinger uncertainty principles give lower bounds for the product of variances $Var_{\rho}(A)\cdot Var_{\rho}(B)$, 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{\"o}dinger form where the bound for the product of variances $Var_{\rho}(A)\cdot Var_{\rho}(B)$ depends on the area spanned by the commutators $[\rho,A]$ and $[\rho,B]$ with respect to an arbitrary quantum version of the Fisher information.

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