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Gribling S, de Laat D, Laurent M. Bounds on entanglement dimensions and quantum graph parameters via noncommutative polynomial optimization. Math Program. 2018;170(1):5-42doi: 10.1007/s10107-018-1287-z.
Gribling, S., de Laat, D., & Laurent, M. (2018). Bounds on entanglement dimensions and quantum graph parameters via noncommutative polynomial optimization. Mathematical programming, 170(1), 5-42. https://doi.org/10.1007/s10107-018-1287-z
Gribling, Sander, et al. "Bounds on entanglement dimensions and quantum graph parameters via noncommutative polynomial optimization." Mathematical programming vol. 170,1 (2018): 5-42. doi: https://doi.org/10.1007/s10107-018-1287-z
Gribling S, de Laat D, Laurent M. Bounds on entanglement dimensions and quantum graph parameters via noncommutative polynomial optimization. Math Program. 2018;170(1):5-42. doi: 10.1007/s10107-018-1287-z. Epub 2018 May 21. PMID: 30996477; PMCID: PMC6435212.
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Math Program. 2018;170(1):5-42. doi: 10.1007/s10107-018-1287-z. Epub 2018 May 21.

Bounds on entanglement dimensions and quantum graph parameters via noncommutative polynomial optimization.

Mathematical programming

Sander Gribling, David de Laat, Monique Laurent

Affiliations

  1. 1CWI, Amsterdam, Netherlands.
  2. 2Tilburg University, Tilburg, Netherlands.

PMID: 30996477 PMCID: PMC6435212 DOI: 10.1007/s10107-018-1287-z

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.

Keywords: Entanglement dimension; Polynomial optimization; Quantum correlation; Quantum graph parameters

References

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  3. Phys Rev Lett. 2015 Jul 10;115(2):020501 - PubMed
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