Groups, Platonic solids and Bell inequalities

Katarzyna Bolonek-Lasoń1 and Piotr Kosiński2

1Department of Statistical Methods, Faculty of Economics and Sociology University of Lodz, 41/43 Rewolucji 1905 St., 90-214 Lodz, Poland
2Department of Computer Science, Faculty of Physics and Applied Informatics University of Lodz, 149/153 Pomorska St., 90-236 Lodz, Poland

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Abstract

The construction of Bell inequalities based on Platonic and Archimedean solids (Quantum 4 (2020), 293) is generalized to the case of orbits generated by the action of some finite groups. A number of examples with considerable violation of Bell inequalities is presented.

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► References

[1] J.S. Bell, Physics 1, 195 (1964).
https:/​/​doi.org/​10.1103/​PhysicsPhysiqueFizika.1.195

[2] Y-C. Liang, R. Spekkens, H. Wiseman, Phys. Rep. 506 (1-2), 1 (2011).
https:/​/​doi.org/​10.1016/​j.physrep.2011.05.001

[3] N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani, S. Wehner, Rev. Mod. Phys. 86, 419 (2014).
https:/​/​doi.org/​10.1103/​RevModPhys.86.419

[4] V.U. Güney, M. Hillery, Phys. Rev. A90, 062121 (2014).
https:/​/​doi.org/​10.1103/​PhysRevA.90.062121

[5] V.U. Güney, M. Hillery, Phys. Rev. A91, 052110 (2015).
https:/​/​doi.org/​10.1103/​PhysRevA.91.052110

[6] K. Bolonek-Lasoń, Phys. Rev. A94, 022107 (2016).
https:/​/​doi.org/​10.1103/​PhysRevA.94.022107

[7] K. Bolonek-Lasoń, Ścibór Sobieski, Quantum Inf. Process. 16, 38 (2017).
https:/​/​doi.org/​10.1007/​s11128-016-1470-1

[8] K. Bolonek-Lasoń, P. Kosiński, Phys. Rev. A99, 052122 (2019).
https:/​/​doi.org/​10.1103/​PhysRevA.99.052122

[9] K. Bolonek-Lasoń, P. Kosiński, Quantum Inf. Process. 19, 63 (2020).
https:/​/​doi.org/​10.1007/​s11128-019-2557-2

[10] A. Fine, Phys. Rev. Lett. 48, 291 (1982).
https:/​/​doi.org/​10.1103/​PhysRevLett.48.291

[11] A. Tavakoli, N. Gisin, Quantum 4, 293 (2020).
https:/​/​doi.org/​10.22331/​q-2020-07-09-293

[12] M. Hamermesh, Group Theory and its Application to Physical Problems, Pergamon Press, (1962).

[13] S. Hossenfelder, Lost in Math: How Beauty Leads Physics Astray, Basic Book, (2018).
https:/​/​doi.org/​10.1007/​s00016-019-00233-0

[14] T. Vertesi, Phys. Rev. A78, 032112 (2008).
https:/​/​doi.org/​10.1103/​PhysRevA.78.032112

[15] S. Brierley, M. Navascues, T. Vertesi, Convex separation from convex optimization for large-scale problems, arXiv:1609.05011.
arXiv:1609.05011

[16] A. Peres, Found. Phys. 29, 589 (1999).
https:/​/​doi.org/​10.1023/​A:1018816310000

[17] T. Vertesi, N. Brunner, Nature Communications 5, 5297 (2014).
https:/​/​doi.org/​10.1038/​ncomms6297

Cited by

[1] Junseo Lee and Kabgyun Jeong, "High-dimensional Private Quantum Channels and Regular Polytopes", Communications in Physics 31 2, 189 (2021).

[2] José I. Latorre and Germán Sierra, "Platonic Entanglement", arXiv:2107.04329.

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