A Generalization of KochenSpecker Sets Relates Quantum Coloring to EntanglementAssisted Channel Capacity
Abstract
We introduce two generalizations of KochenSpecker (KS) sets: projective KS sets and generalized KS sets. We then use projective KS sets to characterize all graphs for which the chromatic number is strictly larger than the quantum chromatic number. Here, the quantum chromatic number is defined via a nonlocal game based on graph coloring. We further show that from any graph with separation between these two quantities, one can construct a classical channel for which entanglement assistance increases the oneshot zeroerror capacity. As an example, we exhibit a new family of classical channels with an exponential increase.
 Publication:

arXiv eprints
 Pub Date:
 July 2012
 DOI:
 10.48550/arXiv.1207.1111
 arXiv:
 arXiv:1207.1111
 Bibcode:
 2012arXiv1207.1111M
 Keywords:

 Quantum Physics;
 Mathematics  Combinatorics
 EPrint:
 16 pages