Coherent states with minimum Gini uncertainty for finite quantum systems

Uncertainty relations $Δ(ρ)\ge η_d$ in terms of the Gini index are studied. The `Gini uncertainty constant' $η_d$ is estimated numerically and compared to an upper bound $\tilde η_d\ge η_d$. It is shown that for large $d$ we get $\tilde η_d\approx η_d$. States $\ket{g}$ with minimum Gini uncertainty and displacement transformations are used to define coherent states $\ket{α, β}_g$ (where $α, β\in {\mathbb Z}_d$) with minimum Gini uncertainty ($Δ[\ket{α, β}_g\;_g\bra{α, β}]\approx η_d$). The $\ket{α, β}_g$ resolve the identity, and therefore an arbitrary state can be expanded in terms of them. This expansion is robust in the presence of noise.

No reviews yet.

No comments yet.