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|Title:||Graph homomorphisms for quantum players||Authors:||Mančinska, Laura
|Issue Date:||2014||Source:||Mančinska, L., & Roberson, D. (2014). Graph homomorphisms for quantum players. LIPIcs–Leibniz International Proceedings in Informatics, 212-216. doi:10.4230/LIPIcs.TQC.2014.212||Series/Report no.:||LIPIcs–Leibniz International Proceedings in Informatics||Abstract:||A homomorphism from a graph X to a graph Y is an adjacency preserving mapping f:V(X) -> V(Y). We consider a nonlocal game in which Alice and Bob are trying to convince a verifier with certainty that a graph X admits a homomorphism to Y. This is a generalization of the well-studied graph coloring game. Via systematic study of quantum homomorphisms we prove new results for graph coloring. Most importantly, we show that the Lovász theta number of the complement lower bounds the quantum chromatic number, which itself is not known to be computable. We also show that other quantum graph parameters, such as quantum independence number, can differ from their classical counterparts. Finally, we show that quantum homomorphisms closely relate to zero-error channel capacity. In particular, we use quantum homomorphisms to construct graphs for which entanglement-assistance increases their one-shot zero-error capacity.||URI:||https://hdl.handle.net/10356/87672
|DOI:||http://dx.doi.org/10.4230/LIPIcs.TQC.2014.212||Rights:||© 2014 The Author(s) (Leibniz International Proceedings in Informatics). Licensed under Creative Commons License CC-BY.||Fulltext Permission:||open||Fulltext Availability:||With Fulltext|
|Appears in Collections:||SPMS Journal Articles|
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