PIRSA:12090073 Scientific Series

DOI10.48660/12090073

Series: Perimeter Institute Quantum Discussions

Mancinska, L. (2012). A generalization of Kochen-Specker sets. Perimeter Institute. https://pirsa.org/12090073

Mancinska, Laura. A generalization of Kochen-Specker sets. Perimeter Institute, Sep. 24, 2012, https://pirsa.org/12090073 

@misc{ pirsa_PIRSA:12090073,
  doi = {10.48660/12090073},
  url = {https://pirsa.org/12090073},
  author = {Mancinska, Laura},
  keywords = {},
  language = {en},
  title = {A generalization of Kochen-Specker sets},
  publisher = {Perimeter Institute},
  year = {2012},
  month = {sep},
  note = {PIRSA:12090073 see, \url{https://pirsa.org}}
}

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.

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