On the quantum chromatic number of a graph
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. We establish relations with the clique number and orthogonal representations of the graph and prove several general facts about this graph parameter. We 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.
P.J.Cameron A.Montanaro M.W.Newman S.Severini A.Winter
School of Mathematical Sciences, Queen Mary, University of London, London E1 4NS, U.K. Department of Computer Science, University of Bristol, Bristol BS8 1UB, U.K. Department of Mathematics, University of York, York YO10 5DD, U.K. Department of Mathematics, University of Bristol, Bristol BS8 1TW, U.K.
国际会议
Asian Conference on Quantum Onformation Science 2006(2006亚洲量子信息大会)
北京
英文
70-71
2006-09-01（万方平台首次上网日期，不代表论文的发表时间）