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Uniqueness of all fundamental noncontextuality inequalities
Physical Review Research Pub Date : 2020-07-02 , DOI: 10.1103/physrevresearch.2.033010
Kishor Bharti , Atul Singh Arora , Leong Chuan Kwek , Jérémie Roland

Contextuality is one way of capturing the nonclassicality of quantum theory. The contextual nature of a theory is often witnessed via the violation of noncontextuality inequalities—certain linear inequalities involving probabilities of measurement events. Using the exclusivity graph approach (one of the two main graph theoretic approaches for studying contextuality), it was shown [Cabello et al. Phys. Rev. A 88, 032104 (2013); Chudnovsky et al. Ann. Math. 164, 51 (2006)] that a necessary and sufficient condition for witnessing contextuality is the presence of an odd number of events (greater than three) which are either cyclically or anticyclically exclusive. Thus, the noncontextuality inequalities the underlying exclusivity structure of which is as stated, either cyclic or anticyclic, are fundamental to quantum theory. We show that there is a unique noncontextuality inequality for each nontrivial cycle and anticycle. In addition to the foundational interest, we expect this to aid the understanding of contextuality as a resource to quantum computing and its applications to local self-testing.

中文翻译:

所有基本的非上下文不等式的唯一性

语境性是捕捉量子理论非经典性的一种方式。理论的上下文性质通常是通过违反非上下文不等式来证明的-某些线性不等式涉及测量事件的概率。使用排他性图方法(研究上下文的两种主要的图论方法之一)进行了显示[Cabello等。 物理 修订版A 88,032104(2013); Chudnovsky等。 安 数学。 164,第51页(2006)],见证上下文的必要和充分条件是存在奇数个事件(大于三个),这些事件是循环或反循环排斥的。因此,其潜在的排他性结构是循环的或反循环的非上下文不等式是量子理论的基础。我们表明,对于每个非平凡的循环和反循环,都有一个唯一的非上下文无关性。除了基本兴趣外,我们希望这有助于理解上下文,这是量子计算及其在局部自测试中的一种资源。
更新日期:2020-07-02
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