Randomness versus nonlocality in the Mermin-Bell experiment with three parties

Erik Woodhead; Boris Bourdoncle; Antonio Acín

doi:10.22331/q-2018-08-17-82

Randomness versus nonlocality in the Mermin-Bell experiment with three parties

Erik Woodhead¹, Boris Bourdoncle¹, and Antonio Acín^1,2

¹ICFO - Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
²ICREA - Institució Catalana de Recerca i Estudis Avançats, Lluis Companys 23, 08010 Barcelona, Spain

Published:	2018-08-17, volume 2, page 82
Eprint:	arXiv:1804.09733v2
Doi:	https://doi.org/10.22331/q-2018-08-17-82
Citation:	Quantum 2, 82 (2018).

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Abstract

The detection of nonlocal correlations in a Bell experiment implies almost by definition some intrinsic randomness in the measurement outcomes. For given correlations, or for a given Bell violation, the amount of randomness predicted by quantum physics, quantified by the guessing probability, can generally be bounded numerically. However, currently only a few exact analytic solutions are known for violations of the bipartite Clauser-Horne-Shimony-Holt Bell inequality. Here, we study the randomness in a Bell experiment where three parties test the tripartite Mermin-Bell inequality. We give tight upper bounds on the guessing probabilities associated with one and two of the parties' measurement outcomes as a function of the Mermin inequality violation. Finally, we discuss the possibility of device-independent secret sharing based on the Mermin inequality and argue that the idea seems unlikely to work.

► BibTeX data

@article{Woodhead2018randomnessversus,
  doi = {10.22331/q-2018-08-17-82},
  url = {https://doi.org/10.22331/q-2018-08-17-82},
  title = {Randomness versus nonlocality in the {M}ermin-{B}ell experiment with three parties},
  author = {Woodhead, Erik and Bourdoncle, Boris and Ac{\'{i}}n, Antonio},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {2},
  pages = {82},
  month = aug,
  year = {2018}
}

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arXiv:1504.06960

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https://doi.org/10.1103/PhysRevA.59.1829
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https://doi.org/10.1119/1.16243

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arXiv:1101.2477

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[3] Federico Grasselli, Quantum Science and Technology 105 (2021) ISBN:978-3-030-64359-1.

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[9] M. G. M. Moreno, Samuraí Brito, Ranieri V. Nery, and Rafael Chaves, "Device-independent secret sharing and a stronger form of Bell nonlocality", Physical Review A 101 5, 052339 (2020).

[10] Yi Li, Yu Xiang, Xiao-Dong Yu, H. Chau Nguyen, Otfried Gühne, and Qiongyi He, "Randomness Certification from Multipartite Quantum Steering for Arbitrary Dimensional Systems", Physical Review Letters 132 8, 080201 (2024).

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[12] Cameron Foreman, Sherilyn Wright, Alec Edgington, Mario Berta, and Florian J. Curchod, "Practical randomness amplification and privatisation with implementations on quantum computers", arXiv:2009.06551, (2020).

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