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QUANTUM GRAPH HOMOMORPHISMS VIA OPERATOR SYSTEMS

CARLOS M. ORTIZ, VERN I. PAULSEN

2016enquantumgraphhomomorphismsoperator systemsmathematics

Abstract

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We explore the concept of a graph homomorphism through the lens of C*-algebras and operator systems. We start by studying the various notions of a quantum graph homomorphism and examine how they are related to each other. We then define and study a C*-algebra that encodes all the information about these homomorphisms and establish a connection between computational complexity and the representation of these algebras. We use this C*-algebra to define a new quantum chromatic number and establish some basic properties of this number. We then suggest a way of studying these quantum graph homomorphisms using certain completely positive maps and describe their structure. Finally, we use these completely positive maps to define the notion of a 'quantum' core of a graph.

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Cite This Work

@article{22be422b-aff6-4d18-b7fc-6ee340d25731,
  title={QUANTUM GRAPH HOMOMORPHISMS VIA OPERATOR SYSTEMS},
  author={CARLOS M. ORTIZ and VERN I. PAULSEN},
  year={2016},
  language={en}
}
TY  - JOUR
TI  - QUANTUM GRAPH HOMOMORPHISMS VIA OPERATOR SYSTEMS
AU  - CARLOS M. ORTIZ
AU  - VERN I. PAULSEN
PY  - 2016
LA  - en
ER  -

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