关于图的量子色数
On the quantum chromatic number of a graph
摘要：
我们调查的概念，量子色数的一个图形，这是最小数量的颜色所需的协议中，两个独立的证明者可以说服一个有把握，他们有一个着色的图形。在从第一原理讨论了这个概念之后，我们继续建立与图的团数和正交表示的关系。我们还证明了这个图形参数的几个一般性的事实，并通过随机图寻找团数和量子色数之间的大分离。最后，我们证明了经典色数和量子色数之间没有分离，如果后者是2，也不是如果它是3在一个限制的量子模型;另一方面，我们展示了一个图的18个顶点和44条边的色数5和量子色数4。
英文摘要：
We investigate the notion of quantum chromatic number of a graph, which is the minimal number of colours necessary in a protocol in which two separated provers can convince an interrogator with certainty that they have a colouring of the graph. After discussing this notion from first principles, we go on to establish relations with the clique number and orthogonal representations of the graph. We also prove several general facts about this graph parameter and find large separations between the clique number and the quantum chromatic number by looking at random graphs. Finally, we show that there can be no separation between classical and quantum chromatic number if the latter is 2, nor if it is 3 in a restricted quantum model; on the other hand, we exhibit a graph on 18 vertices and 44 edges with chromatic number 5 and quantum chromatic number 4.
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