论文标题
五角星的一类三数Qubit的上下文配置
A Class of Three-Qubit Contextual Configurations Located in Fano Pentads
论文作者
论文摘要
鉴于$ w（5,2）$的符合性极性空间，让我们称一组五个Fano飞机共享成对的一点点是Fano Pentad。一旦63点$ w（5,2）$被63个非平凡的三Q量观测值适当地标记，任何此类fano pentad都会产生一种称为Mermin Pentagram的量子上下文集。在这里，显示出Fano Pentad还托管了另一个密切相关的上下文集，该集合具有25个可观察结果和30个三元元素上下文。在25个可观察到的中，有十个使每个上下文都在六个上下文中，而其余15个可观察到的物品中的每一个仅属于两个上下文。利用了Mermin Pentagrams的最新分类（Saniga等人，对称性12（2020）534），发现12,096此类上下文集构成了47种不同类型，根据数量（$ 3、5、5、7，\ ldots，17 $）掉入八个家庭。
Given the symplectic polar space of type $W(5,2)$, let us call a set of five Fano planes sharing pairwise a single point a Fano pentad. Once 63 points of $W(5,2)$ are appropriately labeled by 63 non-trivial three-qubit observables, any such Fano pentad gives rise to a quantum contextual set known as Mermin pentagram. Here, it is shown that a Fano pentad also hosts another, closely related contextual set, which features 25 observables and 30 three-element contexts. Out of 25 observables, ten are such that each of them is on six contexts, while each of the remaining 15 observables belongs to two contexts only. Making use of the recent classification of Mermin pentagrams (Saniga et al., Symmetry 12 (2020) 534), it was found that 12,096 such contextual sets comprise 47 distinct types, falling into eight families according to the number ($3, 5, 7, \ldots, 17$) of negative contexts.
