Symmetric multipartite Bell inequalities via Frank-Wolfe algorithms

Abstract

In multipartite Bell scenarios, we study the nonlocality robustness of the Greenberger-Horne-Zeilinger (GHZ) state. When each party performs planar measurements forming a regular polygon, we exploit the symmetry of the resulting correlation tensor to drastically accelerate the computation of (i) a Bell inequality via Frank-Wolfe algorithms, and (ii) the corresponding local bound. The Bell inequalities obtained are facets of the symmetrised local polytope and they give the best known upper bounds on the nonlocality robustness of the GHZ state for three to ten parties. Moreover, for four measurements per party, we generalise our facets and hence show, for any number of parties, an improvement on Mermin's inequality in terms of noise robustness. We also compute the detection efficiency of our inequalities and show that some give rise to activation of nonlocality in star networks, a property that was only shown with an infinite number of measurements.

arXiv comment12 pages, 2 figures

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Cited by in corpus (9)

• Nonlocality activation in a photonic quantum network
• All incompatible measurements on qubits lead to multiparticle Bell nonlocality
• Deriving three-outcome permutationally invariant Bell inequalities
• Device-Independent Certification of Multipartite Distillable Entanglement
• Improved algorithms and novel applications of the FrankWolfe.jl library
• Detection Efficiency Bounds in (Semi-)Device-Independent Scenarios
• Symmetric observations without symmetric causal explanations
• Classical bounds on two-outcome bipartite Bell expressions and linear prepare-and-measure witnesses: Efficient computation in parallel environments such as graphics processing units
• Better bounds on finite-order Grothendieck constants