Experimentally friendly approach towards nonlocal correlations in multisetting N-partite Bell scenarios

Artur Barasiński; Antonín Černoch; Wiesław Laskowski; Karel Lemr; Tamás Vértesi; Jan Soubusta

doi:10.22331/q-2021-04-14-430

Experimentally friendly approach towards nonlocal correlations in multisetting N-partite Bell scenarios

Artur Barasiński^1,2, Antonín Černoch³, Wiesław Laskowski^4,5, Karel Lemr², Tamás Vértesi⁶, and Jan Soubusta²

¹Institute of Theoretical Physics, Uniwersity of Wroclaw, Plac Maxa Borna 9, 50-204 Wrocław, Poland
²RCPTM, Joint Laboratory of Optics of Palacký University and Institute of Physics of CAS, Faculty of Science, Palacký University, 17. listopadu 12, 771 46 Olomouc, Czech Republic
³Institute of Physics of the Czech Academy of Sciences, Joint Laboratory of Optics of Palacký University and Institute of Physics of CAS, 17. listopadu 50A, 772 07 Olomouc, Czech Republic
⁴Institute of Theoretical Physics and Astrophysics, Faculty of Mathematics, Physics and Informatics, University of Gdańsk, 80-308 Gdańsk, Poland
⁵International Centre for Theory of Quantum Technologies, University of Gdańsk, 80-308 Gdańsk, Poland
⁶MTA Atomki Lendület Quantum Correlations Research Group, Institute for Nuclear Research, P.O. Box 51, H-4001 Debrecen, Hungary

Published:	2021-04-14, volume 5, page 430
Eprint:	arXiv:2009.11691v2
Doi:	https://doi.org/10.22331/q-2021-04-14-430
Citation:	Quantum 5, 430 (2021).

Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.

Abstract

In this work, we study a recently proposed operational measure of nonlocality by Fonseca and Parisio [Phys. Rev. A 92, 030101(R) (2015)] which describes the probability of violation of local realism under randomly sampled observables, and the strength of such violation as described by resistance to white noise admixture. While our knowledge concerning these quantities is well established from a theoretical point of view, the experimental counterpart is a considerably harder task and very little has been done in this field. It is caused by the lack of complete knowledge about the facets of the local polytope required for the analysis. In this paper, we propose a simple procedure towards experimentally determining both quantities for $N$-qubit pure states, based on the incomplete set of tight Bell inequalities. We show that the imprecision arising from this approach is of similar magnitude as the potential measurement errors. We also show that even with both a randomly chosen $N$-qubit pure state and randomly chosen measurement bases, a violation of local realism can be detected experimentally almost $100\%$ of the time. Among other applications, our work provides a feasible alternative for the witnessing of genuine multipartite entanglement without aligned reference frames.

► BibTeX data

@article{Barasinski2021experimentally,
  doi = {10.22331/q-2021-04-14-430},
  url = {https://doi.org/10.22331/q-2021-04-14-430},
  title = {Experimentally friendly approach towards nonlocal correlations in multisetting {N}-partite {B}ell scenarios},
  author = {Barasi{\'{n}}ski, Artur and {\v{C}}ernoch, Anton{\'{i}}n and Laskowski, Wies{\l{}}aw and Lemr, Karel and V{\'{e}}rtesi, Tam{\'{a}}s and Soubusta, Jan},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {5},
  pages = {430},
  month = apr,
  year = {2021}
}

► References

[1] J. S. Bell. On the eistein podolsky rosen paradox. Physics, 1: 195, 1964. 10.1103/PhysicsPhysiqueFizika.1.195.
https://doi.org/10.1103/PhysicsPhysiqueFizika.1.195

[2] A. Einstein, B. Podolsky, and N. Rosen. Can quantum-mechanical description of physical reality be considered complete? Phys. Rev., 47: 777, 1935. 10.1103/PhysRev.47.777.
https://doi.org/10.1103/PhysRev.47.777

[3] A. Aspect. Bell's inequality test: more ideal than ever. Nature, 398: 189, 1999. https://doi.org/10.1038/18296.
https://doi.org/10.1038/18296

[4] N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani, and S. Wehner. Bell nonlocality. Rev. Mod. Phys., 86: 419, 2014. 10.1103/RevModPhys.86.419.
https://doi.org/10.1103/RevModPhys.86.419

[5] C. H. Bennet and G. Brassard. Quantum cryptography: Public key distribution and coin tossing. In Proceedings of IEEE International Conference on Computers, Systems and Signal Processing, page 175, New York, USA, 1984. IEEE.

[6] Artur K. Ekert. Quantum cryptography based on bell's theorem. Phys. Rev. Lett., 67: 661, 1991. 10.1103/PhysRevLett.67.661.
https://doi.org/10.1103/PhysRevLett.67.661

[7] Harry Buhrman, Richard Cleve, Serge Massar, and Ronald de Wolf. Nonlocality and communication complexity. Rev. Mod. Phys., 82: 665, 2010. 10.1103/RevModPhys.82.665.
https://doi.org/10.1103/RevModPhys.82.665

[8] S. Pironio, A. Acín, S. Massar, A. Boyer de la Giroday, D. N. Matsukevich, P. Maunz, S. Olmschenk, D. Hayes, L. Luo, T. A. Manning, and C. Monroe. Random numbers certified by bell’s theorem. Nature, 464: 1021, 2010. https://doi.org/10.1038/nature09008.
https://doi.org/10.1038/nature09008

[9] A. Acín, N. Brunner, N. Gisin, S. Massar, S. Pironio, and V. Scarani. Device-independent security of quantum cryptography against collective attacks. Phys. Rev. Lett., 98: 230501, 2007. 10.1103/PhysRevLett.98.230501.
https://doi.org/10.1103/PhysRevLett.98.230501

[10] Rafael Rabelo, Melvyn Ho, Daniel Cavalcanti, Nicolas Brunner, and Valerio Scarani. Device-independent certification of entangled measurements. Phys. Rev. Lett., 107: 050502, 2011. 10.1103/PhysRevLett.107.050502.
https://doi.org/10.1103/PhysRevLett.107.050502

[11] A. A. Méthot and V. Scarani. An anomaly of non-locality. Quantum Inf. Comput., 7: 157, 2007.

[12] Y.-C. Liang, N. Harrigan, S. D. Bartlett, and T. Rudolph. Nonclassical correlations from randomly chosen local measurements. Phys. Rev. Lett., 104: 050401, 2010. 10.1103/PhysRevLett.104.050401.
https://doi.org/10.1103/PhysRevLett.104.050401

[13] J. J. Wallman, Y.-C. Liang, and S. D. Bartlett. Generating nonclassical correlations without fully aligning measurements. Phys. Rev. A, 83: 022110, 2011. 10.1103/PhysRevA.83.022110.
https://doi.org/10.1103/PhysRevA.83.022110

[14] E. A. Fonseca and F. Parisio. Measure of nonlocality which is maximal for maximally entangled qutrits. Phys. Rev. A, 92: 030101(R), 2015. 10.1103/PhysRevA.92.030101.
https://doi.org/10.1103/PhysRevA.92.030101

[15] A. de Rosier, J. Gruca, F. Parisio, T. Vértesi, and W. Laskowski. Multipartite nonlocality and random measurements. Phys. Rev. A, 96: 012101, 2017. 10.1103/PhysRevA.96.012101.
https://doi.org/10.1103/PhysRevA.96.012101

[16] Artur Barasiński and Mateusz Nowotarski. Volume of violation of bell-type inequalities as a measure of nonlocality. Phys. Rev. A, 98: 022132, 2018. 10.1103/PhysRevA.98.022132.
https://doi.org/10.1103/PhysRevA.98.022132

[17] Alejandro Fonseca, Anna de Rosier, Tamás Vértesi, Wiesław Laskowski, and Fernando Parisio. Survey on the bell nonlocality of a pair of entangled qudits. Phys. Rev. A, 98: 042105, 2018. 10.1103/PhysRevA.98.042105.
https://doi.org/10.1103/PhysRevA.98.042105

[18] Artur Barasiński, Antonín Černoch, Karel Lemr, and Jan Soubusta. Genuine tripartite nonlocality for random measurements in greenberger-horne-zeilinger-class states and its experimental test. Phys. Rev. A, 101: 052109, 2020. 10.1103/PhysRevA.101.052109.
https://doi.org/10.1103/PhysRevA.101.052109

[19] V. Lipinska, F. Curchod, A. Máttar, and A. Acín. Towards an equivalence between maximal entanglement and maximal quantum nonlocality. New J. Phys., 20: 063043, 2018. 10.1088/1367-2630/aaca22.
https://doi.org/10.1088/1367-2630/aaca22

[20] Anna de Rosier, Jacek Gruca, Fernando Parisio, Tamás Vértesi, and Wiesław Laskowski. Strength and typicality of nonlocality in multisetting and multipartite bell scenarios. Phys. Rev. A, 101: 012116, 2020. 10.1103/PhysRevA.101.012116.
https://doi.org/10.1103/PhysRevA.101.012116

[21] Thomas Cope and Roger Colbeck. Bell inequalities from no-signaling distributions. Phys. Rev. A, 100: 022114, 2019. 10.1103/PhysRevA.100.022114.
https://doi.org/10.1103/PhysRevA.100.022114

[22] Shih-Xian Yang, Gelo Noel Tabia, Pei-Sheng Lin, and Yeong-Cherng Liang. Device-independent certification of multipartite entanglement using measurements performed in randomly chosen triads. Phys. Rev. A, 102: 022419, 2020. 10.1103/PhysRevA.102.022419.
https://doi.org/10.1103/PhysRevA.102.022419

[23] Jacek Gruca, Wiesław Laskowski, Marek Żukowski, Nikolai Kiesel, Witlef Wieczorek, Christian Schmid, and Harald Weinfurter. Nonclassicality thresholds for multiqubit states: Numerical analysis. Phys. Rev. A, 82: 012118, 2010. 10.1103/PhysRevA.82.012118.
https://doi.org/10.1103/PhysRevA.82.012118

[24] Z. Hradil. Quantum-state estimation. Phys. Rev. A, 55: R1561, 1997. 10.1103/PhysRevA.55.R1561.
https://doi.org/10.1103/PhysRevA.55.R1561

[25] Pei-Sheng Lin, Denis Rosset, Yanbao Zhang, Jean-Daniel Bancal, and Yeong-Cherng Liang. Device-independent point estimation from finite data and its application to device-independent property estimation. Phys. Rev. A, 97: 032309, 2018. 10.1103/PhysRevA.97.032309.
https://doi.org/10.1103/PhysRevA.97.032309

[26] P. Shadbolt, T. Vértesi, Y.-C. Liang, C. Branciard, N. Brunner, and J. L. O’Brien. Guaranteed violation of a bell inequality without aligned reference frames or calibrated devices. Sci. Rep., 2: 470, 2012. https://doi.org/10.1038/srep00470.
https://doi.org/10.1038/srep00470

[27] Joshua A Slater, Cyril Branciard, Nicolas Brunner, and Wolfgang Tittel. Device-dependent and device-independent quantum key distribution without a shared reference frame. New J. Phys., 16: 043002, 2014. 10.1088/1367-2630/16/4/043002.
https://doi.org/10.1088/1367-2630/16/4/043002

[28] J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt. Proposed experiment to test local hidden-variable theories. Phys. Rev. Lett., 23: 880, 1969. 10.1103/PhysRevLett.23.880.
https://doi.org/10.1103/PhysRevLett.23.880

[29] I. Pitowsky and K. Svozil. Optimal tests of quantum nonlocality. Phys. Rev. A, 64: 014102, 2001. 10.1103/PhysRevA.64.014102.
https://doi.org/10.1103/PhysRevA.64.014102

[30] C. Śliwa. Symmetries of the bell correlation inequalities. Phys. Lett. A, 317: 165, 2003. 10.1016/S0375-9601(03)01115-0.
https://doi.org/10.1016/S0375-9601(03)01115-0

[31] Stephen Boyd and Lieven Vandenberghe. Convex Optimization. Cambridge University Press, 2004.

[32] I. Pitowsky. Quantum Probability — Quantum Logic, volume 321. Springer-Verlag Berlin Heidelberg, 1989.

[33] S. Pironio. Lifting bell inequalities. J. Math. Phys., 46: 062112, 2005. https://doi.org/10.1063/1.1928727.
https://doi.org/10.1063/1.1928727

[34] W. Laskowski, T. Vértesi, and M. Wieśniak. Highly noise resistant multiqubit quantum correlations. J. Phys. A: Math. Theor., 48: 465301, 2015. https://doi.org/10.1088/1751-8113/48/46/465301.
https://doi.org/10.1088/1751-8113/48/46/465301

[35] Kamil Kostrzewa, Wiesław Laskowski, and Tamás Vértesi. Closing the detection loophole in multipartite bell experiments with a limited number of efficient detectors. Phys. Rev. A, 98: 012138, 2018. 10.1103/PhysRevA.98.012138.
https://doi.org/10.1103/PhysRevA.98.012138

[36] F. J. Curchod, N. Gisin, and Y.-C. Liang. Quantifying multipartite nonlocality via the size of the resource. Phys. Rev. A, 91: 012121, 2015. 10.1103/PhysRevA.91.012121.
https://doi.org/10.1103/PhysRevA.91.012121

[37] C. Jebarathinam, Jui-Chen Hung, Shin-Liang Chen, and Yeong-Cherng Liang. Maximal violation of a broad class of bell inequalities and its implication on self-testing. Phys. Rev. Research, 1: 033073, 2019. 10.1103/PhysRevResearch.1.033073.
https://doi.org/10.1103/PhysRevResearch.1.033073

[38] J. Matoušek, M. Sharir, and E. Welzl. A subexponential bound for linear programming. Algorithmica, 16: 498, 1996. https://doi.org/10.1007/BF01940877.
https://doi.org/10.1007/BF01940877

[39] W. Dür, G. Vidal, and J. I. Cirac. Three qubits can be entangled in two inequivalent ways. Phys. Rev. A, 62: 062314, 2000. 10.1103/PhysRevA.62.062314.
https://doi.org/10.1103/PhysRevA.62.062314

[40] A. Barasiński, A. Černoch, K. Lemr, and J. Soubusta. Experimental verification of time-order-dependent correlations in three-qubit greenberger-horne-zeilinger-class states. Phys. Rev. A, 99: 042123, 2019. 10.1103/PhysRevA.99.042123.
https://doi.org/10.1103/PhysRevA.99.042123

[41] R. F. Werner and M. M. Wolf. All-multipartite bell-correlation inequalities for two dichotomic observables per site. Phys. Rev. A, 64: 032112, 2001. 10.1103/PhysRevA.64.032112.
https://doi.org/10.1103/PhysRevA.64.032112

[42] D. Collins and N. Gisin. A relevant two qubit bell inequality inequivalent to the CHSH inequality. J. Phys. A, 37: 1775, 2004. https://doi.org/10.1088/0305-4470/37/5/021.
https://doi.org/10.1088/0305-4470/37/5/021

[43] M. Hein, J. Eisert, and H. J. Briegel. Multiparty entanglement in graph states. Phys. Rev. A, 69: 062311, 2004. 10.1103/PhysRevA.69.062311.
https://doi.org/10.1103/PhysRevA.69.062311

[44] Paul G. Kwiat, Edo Waks, Andrew G. White, Ian Appelbaum, and Philippe H. Eberhard. Ultrabright source of polarization-entangled photons. Phys. Rev. A, 60: R773, 1999. 10.1103/PhysRevA.69.062311.
https://doi.org/10.1103/PhysRevA.69.062311

[45] Miroslav Ježek, Jaromír Fiurášek, and Zdeněk Hradil. Quantum inference of states and processes. Phys. Rev. A, 68: 012305, 2003. 10.1103/PhysRevA.68.012305.
https://doi.org/10.1103/PhysRevA.68.012305

[46] Antonín Černoch, Jan Soubusta, Lucie Bartůšková, Miloslav Dušek, and Jaromír Fiurášek. Experimental realization of linear-optical partial swap gates. Phys. Rev. Lett., 100: 180501, 2008. 10.1103/PhysRevLett.100.180501.
https://doi.org/10.1103/PhysRevLett.100.180501

[47] K. Życzkowski and M. Kuś. Random unitary matrices. J. Phys. A, 27: 4235, 1994. https://doi.org/10.1088/0305-4470/27/12/028.
https://doi.org/10.1088/0305-4470/27/12/028

Cited by

[1] Kateřina Jiráková, Artur Barasiński, Antonín Černoch, Karel Lemr, and Jan Soubusta, "Measuring Concurrence in Qubit Werner States Without an Aligned Reference Frame", Physical Review Applied 16 5, 054042 (2021).

[2] Ari Patrick, Giulio Camillo, Fernando Parisio, and Barbara Amaral, "Bell-nonlocality quantifiers and their persistent mismatch with the entropy of entanglement", Physical Review A 107 4, 042410 (2023).

[3] Mahasweta Pandit, Artur Barasiński, István Márton, Tamás Vértesi, and Wiesław Laskowski, "Optimal tests of genuine multipartite nonlocality", New Journal of Physics 24 12, 123017 (2022).

[4] Artur Barasiński, Jan Peřina, and Antonín Černoch, "Quantification of Quantum Correlations in Two-Beam Gaussian States Using Photon-Number Measurements", Physical Review Letters 130 4, 043603 (2023).

The above citations are from Crossref's cited-by service (last updated successfully 2023-06-08 08:35:40) and SAO/NASA ADS (last updated successfully 2023-06-08 08:35:40). The list may be incomplete as not all publishers provide suitable and complete citation data.

This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.