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.
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