Symmetric multipartite Bell inequalities via Frank-Wolfe algorithms

Designolle, Sébastien; Vértesi, Tamás; Pokutta, Sebastian

doi:10.1103/PhysRevA.109.022205

Symmetric multipartite Bell inequalities via Frank-Wolfe algorithms

Oct 31, 2023

12 pages

Published in:

Phys.Rev.A 109 (2024) 2, 022205

Published: Feb 7, 2024

e-Print:

2310.20677 [quant-ph]

DOI:

10.1103/PhysRevA.109.022205 (publication)

View in:

ADS Abstract Service

pdf

reference search6 citations

Citations per year

Abstract: (APS)

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 symmetrized 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 generalize 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 the activation of nonlocality in star networks, a property that was only shown with an infinite number of measurements.

Note:

12 pages, 2 figures

References(34)

Figures(1)

[1]

On the Einstein-Podolsky-Rosen paradox

J.S. Bell
(
- Wisconsin U., Madison
)

- Physics Physique Fizika 1 (1964) 195-200
•
DOI:
- 10.1103/PhysicsPhysiqueFizika.1.195

[2]

Proposed experiment to test local hidden variable theories

- Phys.Rev.Lett. 23 (1969) 880-884
•
DOI:
- 10.1103/PhysRevLett.23.880

[3]

Bell nonlocality

Nicolas Brunner
(
- Geneva U. and
- Bristol U.
)
,
Daniel Cavalcanti
(
- Singapore Natl. U. and
- ICFO, Barcelona
)
,
Stefano Pironio
(
- Brussels U.
)
,
Valerio Scarani
(
- Singapore Natl. U.
)
,
Stephanie Wehner
(
- Singapore Natl. U. and
- A-STAR, Singapore
)

- Rev.Mod.Phys. 86 (2014) 419
•
e-Print:
- 1303.2849
•
DOI:
- 10.1103/RevModPhys.86.419

[4]

Oxford Graduate Texts (, New York, )

V. Scarani

[5]

Nonclassicality thresholds for multiqubit states: Numerical analysis

J. Gruca
,
W. Laskowski
,
M. Żukowski
,
N. Kiesel
,
W. Wieczorek

et al.

- Phys.Rev.A 82 (2010) 012118
•
DOI:
- 10.1103/PhysRevA.82.012118

[6]

Solving large-scale optimization problems related to Bell’s Theorem

- J.Comput.Appl.Math. 263 (2014) 392-404
•
DOI:
- 10.1016/j.cam.2013.12.003

[7]

Optimal tests of genuine multipartite nonlocality

Mahasweta Pandit
(
- Gdansk U.
)
,
Artur Barasinski
(
- Palacky U. and
- Wroclaw U.
)
,
Istvan Marton
(
- KLTE-ATOMKI
)
,
Tamas Vertesi
(
- KLTE-ATOMKI
)
,
Wieslaw Laskowski
(
- Gdansk U.
)

- New J.Phys. 24 (2022) 12, 123017
•
e-Print:
- 2206.08848
•
DOI:
- 10.1088/1367-2630/aca8c8

[8]

Convex separation from convex optimization for large-scale problems

S. Brierley
,
M. Navascués
,
T. Vértesi

e-Print:
- 1609.05011

[9]

Improved local models and new Bell inequalities via Frank-Wolfe algorithms

et al.

- Phys.Rev.Res. 5 (2023) 4, 043059
•
e-Print:
- 2302.04721
•
DOI:
- 10.1103/PhysRevResearch.5.043059

[10]

Looking for symmetric Bell inequalities

J.-D. Bancal
,
N. Gisin
,
S. Pironio

- J.Phys.A 43 (2010) 385303
•
DOI:
- 10.1088/1751-8113/43/38/385303

[11]

Entanglement swapping of noisy states: A kind of superadditivity in nonclassicality

A. Sen
,
U. Sen
,
V. Brukner
,
V. Bužek
,
M. Żukowski

- Phys.Rev.A 72 (2005) 042310
•
DOI:
- 10.1103/PhysRevA.72.042310

[12]

Extreme quantum entanglement in a superposition of macroscopically distinct states

N.David Mermin

- Phys.Rev.Lett. 65 (1990) 15, 1838
•
DOI:
- 10.1103/PhysRevLett.65.1838

[13]

Going beyond Bell's theorem, in , edited by (, Dordrecht, ), pp

M. Kafatos
,
D.M. Greenberger
,
M.A. Horne
,
A. Zeilinger

[14]

Nonlocality of three-qubit Greenberger-Horne-Zeilinger–symmetric states

B. Paul
,
K. Mukherjee
,
D. Sarkar

- Phys.Rev.A 94 (2016) 032101
•
DOI:
- 10.1103/PhysRevA.94.032101

[15]

https://oeis.org/A000016

[16]

Bell inequalities: Many questions, a few answers, (, New York, ), pp

N. Gisin

[17]

An iterative procedure for computing the minimum of a quadratic form on a convex set

E.G. Gilbert

- SIAM J. Control 4 (1966) 61
•
DOI:
- 10.1137/0304007

[18]

Conditional gradient methods

G. Braun
,
A. Carderera
,
C.W. Combettes
,
H. Hassani
,
A. Karbasi

et al.

e-Print:
- 2211.14103

[19]

An algorithm for quadratic programming

M. Frank
,
P. Wolfe

- Nav.Res.Logist.Q. 3 (1956) 95
•
DOI:
- 10.1002/nav.3800030109

[20]

Revisiting Frank–Wolfe: Projection-free sparse convex optimization, in Proceedings of the 30th International Conference on Machine Learning, edited by (, ), Vol. 28, p

S. Dasgupta
,
D. McAllester
,
M. Jaggi

[21]

Blended conditional gradients: The unconditioning of conditional gradients

G. Braun
,
S. Pokutta
,
D. Tu
,
S. Wright

e-Print:
- 1805.07311

[22]

Version 4.12.2

T.G. Group

[23]

See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevA.109.022205 for the Bell inequalities and analytical values of the values

[24]

Quantum Pseudo-Telepathy

- Found.Phys. 35 (2005) 11, 1877-1907
•
DOI:
- 10.1007/s10701-005-7353-4

[25]

Grothendieck's constant and local models for noisy entangled quantum states

A. Acín
,
N. Gisin
,
B. Toner

- Phys.Rev.A 73 (2006) 062105
•
DOI:
- 10.1103/PhysRevA.73.062105

1-25 of 34
1
2
25 / page