Coherent states with minimum Gini uncertainty for finite quantum systems

Abstract

Uncertainty relations in terms of the Gini index are studied. The “Gini uncertainty constant” is estimated numerically and compared to an upper bound . It is shown that for large d we get . States with minimum Gini uncertainty and displacement transformations are used to define coherent states (where ) with minimum Gini uncertainty . The resolve the identity, and therefore an arbitrary state can be expanded in terms of them. This expansion is robust in the presence of noise.