Daniele Imparato

Uncertainty principle and quantum Fisher information. II.

Heisenberg and Schrodinger uncertainty principles give lower bounds for the product of variances Varρ(A)Varρ(B) 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 Schrodinger form where the bound for the product of variances Varρ(A)Varρ(B) depends on the area spanned by the commutators i[ρ,A] and i[ρ,B] with respect to an arbitrary quantum version of the Fisher information.

Inequalities for quantum Fisher information

In the paper [16] Luo proved an inequality relating the Wigner-Yanase information and the SLD-information. In this paper we prove that Luo’s inequality is a particular case of a general inequality which holds for any regular quantum Fisher information. Moreover we show that this general inequality is a consequence of the Kubo-Ando inequality that states that any matrix mean is bigger than the harmonic mean and smaller than the arithmetic mean.

Temporal and Spatial Statistical Methods to Remove External Effects on Groundwater Levels

This paper illustrates a project on monitoring groundwater levels elaborated jointly with officers from Regione Piemonte. Groundwater levels are strongly affected by external predictors, such as rain precipitation, neighboring waterways or local irrigation ditches. We discuss a kriging and transfer function approach applied to monthly and daily series of piezometric levels to model these neighboring effects. The aims of the study are to reconstruct a groundwater virgin level as an indicator of the state of health of the groundwater itself and to provide important regulatory tools to the local government.