Does violation of a Bell inequality always imply quantum advantage in a communication complexity problem?

Armin Tavakoli; Marek Żukowski; Časlav Brukner

doi:10.22331/q-2020-09-07-316

Does violation of a Bell inequality always imply quantum advantage in a communication complexity problem?

Armin Tavakoli¹, Marek Żukowski², and Časlav Brukner^3,4

¹Département de Physique Appliquée, Université de Genève, CH-1211 Genève, Switzerland
²International Centre for Theory of Quantum Technologies (ICTQT), University of Gdansk, 80-308 Gdansk, Poland
³Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna, Austria
⁴Institute of Quantum Optics and Quantum Information, Austrian Academy of Sciences, Boltzmanngasse 3, A-1090 Vienna, Austria

Published:	2020-09-07, volume 4, page 316
Eprint:	arXiv:1907.01322v3
Doi:	https://doi.org/10.22331/q-2020-09-07-316
Citation:	Quantum 4, 316 (2020).

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Abstract

Quantum correlations which violate a Bell inequality are presumed to power better-than-classical protocols for solving communication complexity problems (CCPs). How general is this statement? We show that violations of correlation-type Bell inequalities allow advantages in CCPs, when communication protocols are tailored to emulate the Bell no-signaling constraint (by not communicating measurement settings). Abandonment of this restriction on classical models allows us to disprove the main result of, inter alia, [22]; we show that quantum correlations obtained from these communication strategies assisted by a small quantum violation of the CGLMP Bell inequalities do not imply advantages in any CCP in the input/output scenario considered in the reference. More generally, we show that there exists quantum correlations, with nontrivial local marginal probabilities, which violate the $I_{3322}$ Bell inequality, but do not enable a quantum advantange in any CCP, regardless of the communication strategy employed in the quantum protocol, for a scenario with a fixed number of inputs and outputs

► BibTeX data

@article{Tavakoli2020doesviolationofbell,
  doi = {10.22331/q-2020-09-07-316},
  url = {https://doi.org/10.22331/q-2020-09-07-316},
  title = {Does violation of a {B}ell inequality always imply quantum advantage in a communication complexity problem?},
  author = {Tavakoli, Armin and {\.{Z}}ukowski, Marek and Brukner, {\v{C}}aslav},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {4},
  pages = {316},
  month = sep,
  year = {2020}
}

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[4] Fabian Bernards and Otfried Gühne, "Generalizing Optimal Bell Inequalities", Physical Review Letters 125 20, 200401 (2020).

[5] A. K. Pan, "Oblivious communication game, self-testing of projective and nonprojective measurements, and certification of randomness", Physical Review A 104 2, 022212 (2021).

[6] S. Gómez, D. Uzcátegui, I. Machuca, E. S. Gómez, S. P. Walborn, G. Lima, and D. Goyeneche, "Optimal strategy to certify quantum nonlocality", Scientific Reports 11 1, 20489 (2021).

[7] Marcin Wieśniak, "Symmetrized persistency of Bell correlations for Dicke states and GHZ-based mixtures", Scientific Reports 11 1, 14333 (2021).

[8] Zhih-Ahn Jia, Lu Wei, Yu-Chun Wu, and Guang-Can Guo, "Quantum Advantages of Communication Complexity from Bell Nonlocality", Entropy 23 6, 744 (2021).

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[10] Carlos Vieira, Carlos de Gois, Lucas Pollyceno, and Rafael Rabelo, "Interplays between classical and quantum entanglement-assisted communication scenarios", New Journal of Physics 25 11, 113004 (2023).

[11] Joseph Ho, George Moreno, Samuraí Brito, Francesco Graffitti, Christopher L. Morrison, Ranieri Nery, Alexander Pickston, Massimiliano Proietti, Rafael Rabelo, Alessandro Fedrizzi, and Rafael Chaves, "Entanglement-based quantum communication complexity beyond Bell nonlocality", npj Quantum Information 8 1, 13 (2022).

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