Centre for Quantum Technologies, National University of Singapore, Singapore.
Phys Rev Lett. 2012 Aug 3;109(5):050404. doi: 10.1103/PhysRevLett.109.050404. Epub 2012 Aug 1.
In this Letter, we demonstrate that the property of monogamy of Bell violations seen for no-signaling correlations in composite systems can be generalized to the monogamy of contextuality in single systems obeying the Gleason property of no disturbance. We show how one can construct monogamies for contextual inequalities by using the graph-theoretic technique of vertex decomposition of a graph representing a set of measurements into subgraphs of suitable independence numbers that themselves admit a joint probability distribution. After establishing that all the subgraphs that are chordal graphs admit a joint probability distribution, we formulate a precise graph-theoretic condition that gives rise to the monogamy of contextuality. We also show how such monogamies arise within quantum theory for a single four-dimensional system and interpret violation of these relations in terms of a violation of causality. These monogamies can be tested with current experimental techniques.
在这封信件中，我们证明了在复合系统中对于无信号关联的贝尔不等式违背的单性关系可以推广到服从无干扰的格里森性质的单系统中的语境单性关系。我们展示了如何通过使用图论技术将代表一组测量的图分解为具有合适独立性数的子图来构造语境不等式的单性关系，这些子图本身可以接受联合概率分布。在证明了所有的弦图子图都可以接受联合概率分布之后，我们提出了一个精确的图论条件，该条件导致了语境单性关系。我们还展示了在单四个维度系统的量子理论中这些单性关系是如何产生的，并根据因果关系的违背来解释这些关系的违背。这些单性关系可以通过当前的实验技术进行测试。
