Bounds on entanglement dimensions and quantum graph parameters via noncommutative polynomial optimization
Gribling,Sander de Laat,David Laurent,Monique
Gribling,Sander
de Laat,David
Laurent,Monique
Abstract
In this paper we study optimization problems related to bipartite quantum correlations using techniques from tracial noncommutative polynomial optimization. First we consider the problem of finding the minimal entanglement dimension of such correlations. We construct a hierarchy of semidefinite programming lower bounds and show convergence to a new parameter: the minimal average entanglement dimension, which measures the amount of entanglement needed to reproduce a quantum correlation when access to shared randomness is free. Then we study optimization problems over synchronous quantum correlations arising from quantum graph parameters. We introduce semidefinite programming hierarchies and unify existing bounds on quantum chromatic and quantum stability numbers by placing them in the framework of tracial polynomial optimization.
Description
Date
2018-07
Journal Title
Journal ISSN
Volume Title
Publisher
Research Projects
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Journal Issue
Keywords
entanglement dimension, polynomial optimization, quantum graph parameters, quantum correlations
Citation
Gribling, S, de Laat, D & Laurent, M 2018, 'Bounds on entanglement dimensions and quantum graph parameters via noncommutative polynomial optimization', Mathematical Programming, vol. 170, no. 1, pp. 5-42. https://doi.org/10.1007/s10107-018-1287-z
License
info:eu-repo/semantics/openAccess