De Bièvre Stephan
Univ. Lille, CNRS, Inria, UMR 8524 - Laboratoire Paul Painlevé, F-59000 Lille, France.
Phys Rev Lett. 2021 Nov 5;127(19):190404. doi: 10.1103/PhysRevLett.127.190404.
For quantum systems with a finite dimensional Hilbert space of states, we show that the complete incompatibility of two observables-a notion we introduce-is equivalent to the large support uncertainty of all states. The Kirkwood-Dirac (KD) quasiprobability distribution of a state-which depends on the choice of two observables-has emerged in quantum information theory as a tool for assessing nonclassical features of the state that can serve as a resource in quantum protocols. We apply our result to show that, when the two observables are completely incompatible, only states with minimal support uncertainty can be KD classical, all others being KD nonclassical. We illustrate our findings with examples.
对于具有有限维态希尔伯特空间的量子系统，我们证明了两个可观测量的完全不相容性——这是我们引入的一个概念——等同于所有态的大支撑不确定性。态的柯克伍德 - 狄拉克（KD）准概率分布——它取决于两个可观测量的选择——在量子信息理论中已成为一种工具，用于评估态的非经典特征，这些特征可作为量子协议中的一种资源。我们应用我们的结果表明，当两个可观测量完全不相容时，只有具有最小支撑不确定性的态才能是KD经典的，其他所有态都是KD非经典的。我们用例子来说明我们的发现。
