Quantum Graph Homomorphisms via Operator Systems
| Autor: | Vern I. Paulsen, Carlos M. Ortiz |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2015 |
| Předmět: |
Numerical Analysis
Pure mathematics Quantum Physics Algebra and Number Theory Computational complexity theory 010102 general mathematics Mathematics - Operator Algebras FOS: Physical sciences 01 natural sciences Quantum graph 0103 physical sciences FOS: Mathematics Discrete Mathematics and Combinatorics Graph (abstract data type) Homomorphism Graph homomorphism 010307 mathematical physics Geometry and Topology 0101 mathematics Operator Algebras (math.OA) Quantum Physics (quant-ph) Bitwise operation Quantum Mathematics |
| Popis: | 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. Added an appendix, minor corrections, updated contact information |
| Databáze: | OpenAIRE |
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