论文标题
相关性不兼容，非兼容性，不确定性和Kirkwood-dirac非经典性
Relating incompatibility, noncommutativity, uncertainty and Kirkwood-Dirac nonclassicality
论文作者
论文摘要
我们对最近引入的完全不兼容的可观察到的概念及其与纯量子状态的Kirkwood-Dirac非经典性的联系提供了深入的研究。后一个概念最近被证明是量子信息理论和量子计量学中许多问题的核心。在这最后的情况下，结果表明，量子优势需要使用柯克伍德 - 迪拉克非经典状态。我们建立了非常普遍的有效性的尖锐界限，这意味着支持不确定性是有效的柯克伍德 - 迪拉克非古老的见证人。当适应几乎相互无偏见的完全不兼容的可观察到的时，这种结合使我们能够将柯克伍德 - 迪拉克经典状态完全表征为两个可观察到的特征向量。我们还表明，完全不兼容意味着几个弱的不相容概念，其中包括强烈的非兼容性形式。
We provide an in-depth study of the recently introduced notion of completely incompatible observables and its links to the support uncertainty and to the Kirkwood-Dirac nonclassicality of pure quantum states. The latter notion has recently been proven central to a number of issues in quantum information theory and quantum metrology. In this last context, it was shown that a quantum advantage requires the use of Kirkwood-Dirac nonclassical states. We establish sharp bounds of very general validity that imply that the support uncertainty is an efficient Kirkwood-Dirac nonclassicality witness. When adapted to completely incompatible observables that are close to mutually unbiased ones, this bound allows us to fully characterize the Kirkwood-Dirac classical states as the eigenvectors of the two observables. We show furthermore that complete incompatibility implies several weaker notions of incompatibility, among which features a strong form of noncommutativity.
