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Multipartite entanglement versus nonlocality for two families of N−qubit states

Sanchit Srivastava1,2,* and Shohini Ghose1,2,3

  • *Contact author: sanchit.srivastava@uwaterloo.ca
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Phys. Rev. Research 7, 033289 – Published 26 September, 2025

DOI: https://doi.org/10.1103/btbb-p514

Abstract

Entangled states of multiple qubits can violate Bell-type inequalities indicating nonlocal behavior of multiqubit quantum correlations. We analyze the relation between multipartite entanglement and genuine multipartite nonlocality, characterized by Svetlichny inequality violations, for two families of N−qubit states. We show that for the generalized Greenberger-Horne-Zeilinger family of states, Svetlichny inequality is not violated when the n−tangle is less than 1/2 for any even number of qubits. On the other hand, the maximal slice states always violate the Svetlichny inequality when n−tangle is nonzero, and the violation increases monotonically with tangle. Our work generalizes the relations between tangle and Svetlichny inequality violations previously derived for three qubits.

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References (43)

  1. J. S. Bell, On the Einstein Podolsky Rosen paradox, Phys. Phys. Fiz. 1, 195 (1964).
  2. 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).
  3. N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani, and S. Wehner, Bell nonlocality, Rev. Mod. Phys. 86, 419 (2014).
  4. N. Gisin, Bell's inequality holds for all non-product states, Phys. Lett. A 154, 201 (1991).
  5. S. Popescu and D. Rohrlich, Generic quantum nonlocality, Phys. Lett. A 166, 293 (1992).
  6. M. Żukowski, C. Brukner, W. Laskowski, and M. Wiesniak, Do all pure entangled states violate Bell's inequalities for correlation functions? Phys. Rev. Lett. 88, 210402 (2002).
  7. R. Augusiak, M. Demianowicz, J. Tura, and A. Acín, Entanglement and nonlocality are inequivalent for any number of parties, Phys. Rev. Lett. 115, 030404 (2015).
  8. I. Frérot, M. Fadel, and M. Lewenstein, Probing quantum correlations in many-body systems: A review of scalable methods, Rep. Prog. Phys. 86, 114001 (2023).
  9. V. Scarani and N. Gisin, Quantum communication between N-partners and Bell's inequalities, Phys. Rev. Lett. 87, 117901 (2001).
  10. Y. Xiang, Multipartite quantum cryptography based on the violation of Svetlichny's inequality, Eur. Phys. J. D 77, 31 (2023).
  11. M. G. M. Moreno, S. Brito, R. V. Nery, and R. Chaves, Device-independent secret sharing and a stronger form of Bell nonlocality, Phys. Rev. A 101, 052339 (2020).
  12. S. Gangopadhyay, T. Wang, A. Mashatan, and S. Ghose, Controlled quantum teleportation in the presence of an adversary, Phys. Rev. A 106, 052433 (2022).
  13. K. Bharti, M. Ray, Z.-P. Xu, M. Hayashi, L.-C. Kwek, and A. Cabello, Graph-theoretic approach for self-testing in Bell scenarios, PRX Quantum 3, 030344 (2022).
  14. G. Murta and F. Baccari, Self-testing with dishonest parties and device-independent entanglement certification in quantum communication networks, Phys. Rev. Lett. 131, 140201 (2023).
  15. N. Brunner, J. Sharam, and T. Vértesi, Testing the structure of multipartite entanglement with Bell inequalities, Phys. Rev. Lett. 108, 110501 (2012).
  16. T. Moroder, J.-D. Bancal, Y.-C. Liang, M. Hofmann, and O. Gühne, Device-independent entanglement quantification and related applications, Phys. Rev. Lett. 111, 030501 (2013).
  17. S. S. Bhattacharya, B. Paul, A. Roy, A. Mukherjee, C. Jebaratnam, and M. Banik, Improvement in device-independent witnessing of genuine tripartite entanglement by local marginals, Phys. Rev. A 95, 042130 (2017).
  18. T. Holz, H. Kampermann, and D. Bruß, Genuine multipartite Bell inequality for device-independent conference key agreement, Phys. Rev. Res. 2, 023251 (2020).
  19. J.-D. Bancal, N. Gisin, Y.-C. Liang, and S. Pironio, Device-independent witnesses of genuine multipartite entanglement, Phys. Rev. Lett. 106, 250404 (2011).
  20. Q. Y. He and M. D. Reid, Genuine multipartite Einstein-Podolsky-Rosen steering, Phys. Rev. Lett. 111, 250403 (2013).
  21. F. J. Curchod, Y.-C. Liang, and N. Gisin, Multipartite nonlocality as a resource and quantum correlations having indefinite causal order, J. Phys. A: Math. Theor. 47, 424014 (2014).
  22. A. A. Abbott, J. Wechs, F. Costa, and C. Branciard, Genuinely multipartite noncausality, Quantum 1, 39 (2017).
  23. A. Baumeler, A. S. Gilani, and J. Rashid, Unlimited non-causal correlations and their relation to non-locality, Quantum 6, 673 (2022).
  24. B. S. Cirel'son, Quantum generalizations of Bell's inequality, Lett. Math. Phys. 4, 93 (1980).
  25. W. Dür, G. Vidal, and J. I. Cirac, Three qubits can be entangled in two inequivalent ways, Phys. Rev. A 62, 062314 (2000).
  26. H. A. Carteret and A. Sudbery, Local symmetry properties of pure three-qubit states, J. Phys. A: Math. Gen. 33, 4981 (2000).
  27. D. M. Greenberger, M. A. Horne, and A. Zeilinger, in Bell's Theorem, Quantum Theory and Conceptions of the Universe, edited by M. Kafatos (Kluwer Academic Publishers, 1989).
  28. D. Bouwmeester, J.-W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, Observation of three-photon Greenberger-Horne-Zeilinger entanglement, Phys. Rev. Lett. 82, 1345 (1999).
  29. C. F. Roos, M. Riebe, H. Häffner, W. Hänsel, J. Benhelm, G. P. T. Lancaster, C. Becher, F. Schmidt-Kaler, and R. Blatt, Control and measurement of three-qubit entangled states, Science 304, 1478 (2004).
  30. A. Ekert, R. Jozsa, R. Penrose, R. Laflamme, E. Knill, W. H. Zurek, P. Catasti, and S. V. S. Mariappan, NMR Greenberger–Horne–Zeilinger states, Philos. Trans. R. Soc. London Ser. A: Math. Phys. Eng. Sci. 356, 1941 (1998).
  31. G. Svetlichny, Distinguishing three-body from two-body nonseparability by a Bell-type inequality, Phys. Rev. D 35, 3066 (1987).
  32. M. Seevinck and G. Svetlichny, Bell-type inequalities for partial separability in N-particle systems and quantum mechanical violations, Phys. Rev. Lett. 89, 060401 (2002).
  33. D. Collins, N. Gisin, S. Popescu, D. Roberts, and V. Scarani, Bell-type inequalities to detect true n-body nonseparability, Phys. Rev. Lett. 88, 170405 (2002).
  34. J. Batle, C. H. R. Ooi, S. Abdalla, and A. Bagdasaryan, Computing the maximum violation of a Bell inequality is an NP-problem, Quantum Inf. Proc. 15, 2649 (2016).
  35. Y. Xiao, Z. Wang, W.-N. Zhao, and M. Li, Tight upper bound for the maximal expectation value of the N-partite generalized Svetlichny operator, Adv. Quantum Technol. 7, 2400101 (2024).
  36. V. Coffman, J. Kundu, and W. K. Wootters, Distributed entanglement, Phys. Rev. A 61, 052306 (2000).
  37. T. J. Osborne and F. Verstraete, General monogamy inequality for bipartite qubit entanglement, Phys. Rev. Lett. 96, 220503 (2006).
  38. A. Wong and N. Christensen, Potential multiparticle entanglement measure, Phys. Rev. A 63, 044301 (2001).
  39. S. Ghose, N. Sinclair, S. Debnath, P. Rungta, and R. Stock, Tripartite entanglement versus tripartite nonlocality in three-qubit Greenberger-Horne-Zeilinger-class states, Phys. Rev. Lett. 102, 250404 (2009).
  40. A. Ajoy and P. Rungta, Svetlichny's inequality and genuine tripartite nonlocality in three-qubit pure states, Phys. Rev. A 81, 052334 (2010).
  41. J.-D. Bancal, C. Branciard, N. Gisin, and S. Pironio, Quantifying multipartite nonlocality, Phys. Rev. Lett. 103, 090503 (2009).
  42. V. Scarani and N. Gisin, Spectral decomposition of Bell's operators for qubits, J. Phys. A: Math. Gen. 34, 6043 (2001).
  43. A. Miyake, Classification of multipartite entangled states by multidimensional determinants, Phys. Rev. A 67, 012108 (2003).

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Phys. Rev. Research 7, 033289– Published 26 September, 2025
  • Received 28 March 2025
  • Accepted 9 September 2025
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