Skip to main content
SpringerLink
Log in

Quantum gravity and the square of Bell operators

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

The Bell’s inequality is a strong criterion to distinguish classical and quantum mechanical aspects of reality. Its violation is the net effect of the existence of non-locality in systems, an advantage for quantum mechanics over classical physics. The quantum mechanical world is under the control of the Heisenberg uncertainty principle that is generalized by quantum gravity scenarios, called generalized uncertainty principle (GUP). Here, the effects of GUP on the square of Bell operators of qubits and qutrits are studied. The achievements claim that the violation quality of the square of Bell inequalities may be a tool to get a better understanding of the quantum features of gravity. In this regard, it is obtained that the current accuracy of the Stern–Gerlach experiments implies upper bounds on the values of the GUP parameters.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Einstein, E., Podolsky, B., Rosen, N.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777–780 (1935)

    Article  ADS  MATH  Google Scholar 

  2. Bell, J.S.: On the Einstein Podolsky Rosen paradox. Physics (N.Y). 1, 195 (1964)

    MathSciNet  Google Scholar 

  3. Franson, J.D.: Bell inequality for position and time. Phys. Rev. Lett. 62, 2205 (1989)

    Article  ADS  Google Scholar 

  4. Oppenheim, J., Wehner, S.: The uncertainty principle determines the non-locality of quantum mechanics. Science 330, 1072 (2010)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  5. Alsina, D., Cervera, A., Goyeneche, D., Latorre, J.I., Zyczkowski, K.: Operational approach to Bell inequalities: application to qutrits. Phys. Rev. A 94, 0322102 (2016)

    Article  ADS  Google Scholar 

  6. Clauser, J.F., Horne, M.A., Shimony, A., Holt, R.A.: Proposed experiment to test local hidden-variable theories. Phys. Rev. Lett. 23, 880–884 (1969)

    Article  ADS  MATH  Google Scholar 

  7. Heisenberg, W.: Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik. Zeitschr. Phys. 43, 172–198 (1927)

    Article  ADS  MATH  Google Scholar 

  8. Cereceda, J.L.: Mermin’s n-particle Bell inequality and operators’ noncommutativity. Phys. Lett. A 286, 376 (2001)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  9. Wigner, E.P.: On hidden variables and quantum mechanical probabilities. Am. J. Phys. 38, 1005–1009 (1970)

    Article  ADS  Google Scholar 

  10. Clauser, J.F., Horne, M.A.: Experimental consequences of objective local theories. Phys. Rev. D 10, 526–535 (1974)

    Article  ADS  Google Scholar 

  11. Dunningham, J.A., Vedral, V.: Nonlocality of a single particle. Phys. Rev. Lett. 99, 180404 (2007)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  12. Cooper, J.J., Dunningham, J.A.: Single particle nonlocality with completely independent reference states. New J. Phys. 10, 113024 (2008)

    Article  ADS  Google Scholar 

  13. Brunner, N., Cavalcanti, D., Pironio, S., Scarani, V., Wehner, S.: Bell nonlocality. Rev. Mod. Phys. 86, 419 (2014)

    Article  ADS  Google Scholar 

  14. Aspect, A., Grangier, P., Roger, G.: Experimental tests of realistic local theories via Bell’s theorem. Phys. Rev. Lett. 47, 460–463 (1981)

    Article  ADS  Google Scholar 

  15. Aspect, A., Grangier, P., Roger, G.: Experimental realization of Einstein-Podolsky-Rosen-Bohm gedanken experiment: a new violation of Bell’s inequalities. Phys. Rev. Lett. 49, 91 (1982)

  16. Aspect, A., Grangier, P., Roger, G.: Experimental test of Bell’s inequalities using time-varying analyzers. Phys. Rev. Lett. 49, 1804–1807 (1982)

    Article  ADS  MathSciNet  Google Scholar 

  17. Hensen, B., et al.: Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres. Nature 526, 682–686 (2015)

    Article  ADS  Google Scholar 

  18. Acin, A., Chen, J.L., Gisin, N., Kaszlikowski, D., Kwek, L.C., Oh, C.H., Zukowski, M.: Coincidence bell inequality for three three-dimensional systems. Phys. Rev. Lett. 92, 250404 (2004)

    Article  ADS  Google Scholar 

  19. Gisin, N.: Bell’s inequality holds for all non-product states. Phys. Lett. A 154, 201–202 (1991)

    Article  ADS  MathSciNet  Google Scholar 

  20. Gisin, N., Peres, A.: Maximal violation of Bells inequality for arbitrarily large spin. Phys. Lett. A 162, 15–17 (1992)

    Article  ADS  MathSciNet  Google Scholar 

  21. Gisin, N.: Hidden quantum nonlocality revealed by local filters. Phys. Lett. A 210, 151–156 (1996)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  22. Terashima, H., Ueda, M.: Einstein–Podolsky–Rosen correlation seen from moving observers. Quantum Inf. Comput. 3, 224 (2003)

    MathSciNet  MATH  Google Scholar 

  23. Terashima, H., Ueda, M.: Relativistic Einstein–Podolsky–Rosen correlation and Bell’s inequality. Int. J. Quantum Inf. 1, 93 (2003)

    Article  MATH  Google Scholar 

  24. Kim, W.T., Son, E.J.: Lorentz-invariant Bell’s inequality. Phys. Rev. A 71, 014102 (2005)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  25. Friis, N., et al.: Relativistic entanglement of two massive particles. Phys. Rev. A 81, 042114 (2010)

    Article  ADS  Google Scholar 

  26. Moradpour, H., Bahadoran, M., Youplao, P., Yupapin, P., Ghasemi, A.: One and two spin-1/2 particle systems under the Lorentz transformations. J. King Saud Univ. Sci. 30, 506–512 (2018)

    Article  Google Scholar 

  27. Moradpour, H., Maghool, S., Moosavi, S.A.: Three-particle Bell-like inequalities under Lorentz transformations. Quantum Inf. Process. 14, 3913 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  28. Peres, A., Scudo, P.F., Terno, D.R.: Quantum entropy and special relativity. Phys. Rev. Lett. 88, 230402 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  29. Collins, D., Gisin, N., Linden, N., Massar, S., Popescu, S.: Bell inequalities for arbitrarily high-dimensional systems. Phys. Rev. Lett. 88, 040404 (2002)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  30. Vaziri, A., Weihs, G., Zeilinger, A.: Experimental two-photon, three-dimensional entanglement for quantum communication. Phys. Rev. Lett. 89, 240401 (2002)

    Article  ADS  Google Scholar 

  31. Acin, A., Durt, T., Gisin, N., Latorre, J.I.: Quantum non-locality in two three-level systems. Phys. Rev. A 65, 052325 (2002)

    Article  ADS  Google Scholar 

  32. Terashima, H., Ueda, M.: Einstein-Podolsky-Rosen correlation in gravitational field. Phys. Rev. A 69, 032113 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  33. Fuentes-Schuller, I., Mann, R.B.: Alice falls into a black hole: entanglement in noninertial frames. Phys. Rev. Lett. 95, 120404 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  34. Alsing, P.M., Fuentes-Schuller, I., Mann, R.B., Tessier, T.E.: Entanglement of Dirac fields in noninertial frames. Phys. Rev. A 74, 032326 (2006)

    Article  ADS  Google Scholar 

  35. Mann, R.B., Villalba, V.M.: Speeding up entanglement degradation. Phys. Rev. A 80, 022305 (2009)

    Article  ADS  Google Scholar 

  36. Leon, J., Martin-Martinez, E.: Spin and occupation number entanglement of Dirac fields for noninertial observers. Phys. Rev. A 80, 012314 (2009)

    Article  ADS  Google Scholar 

  37. Fuentes, I., Mann, R.B., Martin-Martinez, E., Moradi, S.: Entanglement of Dirac fields in an expanding spacetime. Phys. Rev. D 82, 045030 (2010)

    Article  ADS  Google Scholar 

  38. Smith, A., Mann, R.B.: Persistence of tripartite nonlocality for noninertial observers. Phys. Rev. A 86, 012306 (2012)

    Article  ADS  Google Scholar 

  39. Alsing, P.M., Milburn, G.J.: On entanglement and Lorentz transformations. Quantum Inf. Comput. 2, 487 (2002)

    MathSciNet  MATH  Google Scholar 

  40. Shi, Y.: Entanglement in relativistic quantum field theory. Phys. Rev. D 70, 105001 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  41. Ball, J.L., Schuller, I.F., Schuller, F.P.: Entanglement in an expanding spacetime. Phys. Lett. A 359, 550 (2006)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  42. VerSteeg, G., Menicucci, N.C.: Entangling power of an expanding universe. Phys. Rev. D 79, 044027 (2009)

    Article  ADS  Google Scholar 

  43. Torres-Arenas, A.J., et al.: Entanglement measures of W-state in noninertial frames. Phys. Lett. B 789, 93 (2019)

    Article  ADS  Google Scholar 

  44. Kempf, A., Mangano, G., Mann, R.B.: Hilbert space representation of the minimal length uncertainty relation. Phys. Rev. D 52, 1108 (1995)

    Article  ADS  MathSciNet  Google Scholar 

  45. Nozari, K., Pedram, P.: Minimal length and bouncing-particle spectrum. Europhys. Lett. 92, 50013 (2010)

    Article  ADS  Google Scholar 

  46. Kempf, A.: Noncommutative geometric regularization. Phys. Rev. D 54, 5174 (1996)

    Article  ADS  MathSciNet  Google Scholar 

  47. Bolen, B., Cavaglia, M.: (Anti-)de Sitter Black hole thermodynamics and the generalized uncertainty principle. Gen. Relativ. Grav. 37, 1255 (2005)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  48. Norazi, K., Fazlpour, B.: Generalized uncertainty principle, modified dispersion relations and the early universe thermodynamics. Gen. Relativ. Grav. 38, 1661 (2006)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  49. Chung, W.S., Hassanabadi, H.: New generalized uncertainty principle from the doubly special relativity. Phys. Lett. B 785, 125 (2018)

    Article  ADS  MATH  Google Scholar 

  50. Chung, W.S., Hassanabadi, H.: A new higher order GUP: one dimensional quantum system. Eur. Phys. J. C 79, 213 (2019)

    Article  ADS  Google Scholar 

  51. Roushan, M., Nozari, K.: Particle processes in a discrete spacetime and GW170814 event. Eur. Phys. J. C 79, 212 (2019)

    Article  ADS  Google Scholar 

  52. Aghababaei, S., Moradpour, H., Rezaei, G., Khorshidian, S.: Minimal length, Berry phase and spin-orbit interactions. Phys. Scr. 96, 055303 (2021)

    Article  ADS  Google Scholar 

  53. Moradpour, H., Aghababaei, S., Ziaie, A.H.: A note on effects of generalized and extended uncertainty principles on Jüttner gas. Symmetry 13, 213 (2021)

    Article  Google Scholar 

  54. Casadio, R., Scardigli, F.: Generalized uncertainty principle, classical mechanics, and general relativity. Phys. Lett. B 807, 135558 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  55. Magueijo, J., Smolin, L.: Lorentz invariance with an invariant energy scale. Phys. Rev. Lett. 88, 190403 (2002)

    Article  ADS  Google Scholar 

  56. Magueijo, J., Smolin, L.: String theories with deformed energy-momentum relations, and a possible nontachyonic bosonic string. Phys. Rev. D 71, 026010 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  57. Cortes, J.L., Gamboa, J.: Quantum uncertainty in doubly special relativity. Phys. Rev. D 71, 065015 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  58. Braidotti, M.C., Musslimani, Z.H., Conti, C.: Generalized uncertainty principle and analogue of quantum gravity in optics. Physica D 338, 34–41 (2017)

    Article  ADS  Google Scholar 

  59. Bosso, P., Das, S., Mann, R.B.: Potential tests of the generalized uncertainty principle in the advanced LIGO experiment. Phys. Lett. B 785, 498–505 (2018)

    Article  ADS  Google Scholar 

  60. Bosso, P., Das, S.: Generalized uncertainty principle and angular momentum. Ann. Phys. 383, 416–438 (2017)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  61. Lake, M.J., Miller, M., Liang, Sh.D.: Generalised uncertainty relations for angular momentum and spin in quantum geometry. Universe 6, 56 (2020)

    Article  ADS  Google Scholar 

  62. Brau, F.: Minimal length uncertainty relation and hydrogen atom. J. Phys. A 32, 7691 (1999)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  63. Bauke, H., et al.: What is the relativistic spin operator? New J. Phys. 16(4), 043012 (2014)

    Article  ADS  MATH  Google Scholar 

  64. Ali, A.F., Das, S., Vagenas, E.C.: A proposal for testing quantum gravity in the lab. Phys. Rev. D 84, 044013 (2011)

    Article  ADS  Google Scholar 

  65. Friedrich, B., Herschbach, D.: Stern and Gerlach: How a bad cigar helped reorient atomic physics. Phys. Today 56, 53 (2003)

    Article  ADS  Google Scholar 

  66. Margalit, Y., et al.: Realization of a complete Stern–Gerlach interferometer: toward a test of quantum gravity. Sci. Adv. 7, 22 (2021)

    Article  Google Scholar 

  67. Ghosh, S.: Quantum gravity effects in geodesic motion and predictions of equivalence principle violation. Class. Quantum Gravity 31, 025025 (2014)

    Article  ADS  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

The authors would like to appreciate the anonymous referees for providing useful comments and suggestions that helped us to improve the manuscript. This paper is published as part of a research project supported by the University of Maragheh Research Affairs Office.

Author information

Authors and Affiliations

  1. Department of Physics, Faculty of Sciences, University of Sistan and Baluchestan, Zahedan, Iran

    S. Aghababaei & H. Shabani

  2. Research Institute for Astronomy and Astrophysics of Maragha (RIAAM), University of Maragheh, P.O. Box 55136-553, Maragheh, Iran

    H. Moradpour

Authors
  1. S. Aghababaei
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. H. Moradpour
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. H. Shabani
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to H. Moradpour.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Aghababaei, S., Moradpour, H. & Shabani, H. Quantum gravity and the square of Bell operators. Quantum Inf Process 21, 57 (2022). https://doi.org/10.1007/s11128-021-03397-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-021-03397-2

Keywords

Search

Navigation