On the quantum chromatic number of a graph

Peter J. Cameron*, Ashley Montanaro, Michael W. Newman, Simone Severini, Andreas Winter

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

66 Citations (Scopus)

Abstract

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 a referee 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.

Original languageEnglish
Article numberR81
JournalElectronic Journal of Combinatorics
Volume14
Issue number1 R
Publication statusPublished - 28 Nov 2007

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