Since the uncertainty about an observable of a system prepared in a quantum state is usually described by its variance, when the state is mixed, the variance is a hybrid of quantum and classical uncertainties. Besides that complementarity relations are saturated only for pure, single-quanton, quantum states. For mixed states, the wave–particle quantifiers never saturate the complementarity relation and can even reach zero for a maximally mixed state. So, to fully characterize a quanton it is not sufficient to consider its wave–particle aspect; one has also to regard its correlations with other systems. In this paper, we discuss the relation between quantum correlations and local classical uncertainty measures, as well as the relation between quantum coherence and quantum uncertainty quantifiers. We obtain a complete complementarity relation for quantum uncertainty, classical uncertainty, and predictability. The total quantum uncertainty of a d-paths interferometer is shown to be equivalent to the Wigner–Yanase coherence and the corresponding classical uncertainty is shown to be an entanglement monotone. The duality between complementarity and uncertainty is used to derive quantum correlations measures that complete the complementarity relations for \(l_{1}\)-norm and \(l_{2}\)-norm coherences. Besides, we show that Brukner–Zeilinger’s invariant information quantifies both the wave and particle characters of a quanton and we obtain a sum uncertainty relation for the generalized Gell-Mann’s matrices.

由于在量子状态下准备的系统的可观测量的不确定性通常用其方差来描述，当状态混合时，方差是量子不确定性和经典不确定性的混合。除此之外，互补关系仅对于纯单量子量子态才饱和。对于混合状态，波粒量词永远不会使互补关系饱和，对于最大混合状态甚至可以达到零。因此，要完全表征量子子，仅考虑其波粒方面是不够的；还必须考虑其与其他系统的相关性。在本文中，我们讨论了量子相关性与局域经典不确定性测度之间的关系，以及量子相干性与量子不确定性量词之间的关系。我们获得了量子不确定性、经典不确定性和可预测性的完全互补关系。的总量子不确定性d- paths 干涉仪显示等效于 Wigner-Yanase 相干性，相应的经典不确定性显示为纠缠单调。互补性和不确定性之间的对偶性用于推导出完成\( l_ {1}\) -范数和\( l_ {2}\) -范数相干性的互补关系的量子相关性度量。此外，我们证明 Brukner-Zeilinger 的不变信息量化了一个量子的波和粒子特征，并且我们获得了广义 Gell-Mann 矩阵的和不确定性关系。