A generalization of Kochen-Specker sets



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Recording Details

PIRSA Number: 
12090073

Abstract

I will discuss two
generalizations of Kochen-Specker (KS) sets: projective KS sets and generalized
KS sets. We will see that projective KS sets can be used 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 will further show that from any graph with
separation between these two quantities, one can construct a classical channel
for which entanglement assistance increases the one-shot zero-error capacity.
As an example, we will consider a new family of classical channels with an
exponential increase.