eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2014-12-11
212
216
10.4230/LIPIcs.TQC.2014.212
article
Graph Homomorphisms for Quantum Players
Mancinska, Laura
Roberson, David
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol027-tqc2014/LIPIcs.TQC.2014.212/LIPIcs.TQC.2014.212.pdf
graph homomorphism
nonlocal game
Lovász theta
quantum chromatic number
entanglement