Departamento de Física Aplicada II, Universidad de Sevilla, E-41012 Sevilla, Spain.
Department of Computer Science, and Department of Physics and Astronomy, University College London, WC1E 6BT London, United Kingdom.
Phys Rev Lett. 2014 Jan 31;112(4):040401. doi: 10.1103/PhysRevLett.112.040401. Epub 2014 Jan 27.
Correlations in Bell and noncontextuality inequalities can be expressed as a positive linear combination of probabilities of events. Exclusive events can be represented as adjacent vertices of a graph, so correlations can be associated to a subgraph. We show that the maximum value of the correlations for classical, quantum, and more general theories is the independence number, the Lovász number, and the fractional packing number of this subgraph, respectively. We also show that, for any graph, there is always a correlation experiment such that the set of quantum probabilities is exactly the Grötschel-Lovász-Schrijver theta body. This identifies these combinatorial notions as fundamental physical objects and provides a method for singling out experiments with quantum correlations on demand.
贝尔不等式和非定域性不等式中的相关性可以表示为事件概率的正线性组合。互斥事件可以表示为图的相邻顶点，因此相关性可以与子图相关联。我们表明，经典、量子和更一般理论的相关性最大值分别为这个子图的独立性数、Lovász 数和分数填充数。我们还表明，对于任何图，总是存在一个相关性实验，使得量子概率的集合恰好是 Grötschel-Lovász-Schrijver theta 体。这将这些组合概念确定为基本物理对象，并提供了一种按需挑选具有量子相关性的实验的方法。
