Lovász theta type norms and Operator Systems

Ortiz, Carlos M.; Paulsen, Vern I.

doi:10.48550/arxiv.1412.7101

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Quantum Homomorphisms and Cp Maps1

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2016

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“…Recall [12] that the operator system of a graph G on n vertices is the subspace of the n × n complex matrices M n given by…”

Section: Quantum Homomorphisms and Cp Mapsmentioning

confidence: 99%

Quantum graph homomorphisms via operator systems

Ortiz

Paulsen

2016

Linear Algebra and its Applications

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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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“…Recall [12] that the operator system of a graph G on n vertices is the subspace of the n × n complex matrices M n given by…”

Section: Quantum Homomorphisms and Cp Mapsmentioning

confidence: 99%