论文标题
有限量子系统的最小GINI不确定性的连贯状态
Coherent states with minimum Gini uncertainty for finite quantum systems
论文作者
论文摘要
研究了Gini指数的不确定性关系$δ（ρ）\geη_d$。 “ Gini不确定性常数” $η_d$是数值估计的，并将其与上限$ \ tildeη_d\geη_d$进行比较。结果表明，对于大$ d $，我们得到$ \ tildeη_d\ oit houtη_d$。状态$ \ ket {g} $具有最低gini的不确定性和位移变换来定义连贯的状态$ \ ket {α，β} _g $（其中$α，β\ in {\ Mathbb z} _d $）用最小的gini nock nockimimim gini nock nock nock n of gini noce（$ gini noce） β} _g \; _ g \ bra {α，β}] \大约η_d$）。 $ \ ket {α，β} _g $解决了身份，因此可以根据其扩展任意状态。在存在噪声的情况下，这种扩展是可靠的。
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.
