Skip to main content
Log in

Spin Squeezing Criterion with Local Unitary Invariance

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

We propose a spin squeezing criterion for arbitrary multi-qubit states that is invariant under local unitary operations. We find that, for arbitrary pure two-qubit states, spin squeezing is equivalent to entanglement, and multi-qubit states are entangled if this new spin squeezing parameter is less than unity.

PACS: 03.67.-a; 03.65.Ud

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

REFERENCES

  1. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, 2000).

  2. D. Bouwmeester, A. Ekert, and A. Zeilinger, The Physics of Quantum Information: Quantum Cryptography, Quantum Teleportation, Quantum Computation (Springer-Verlag, Berlin, 2000).

    Google Scholar 

  3. C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W. K. Wootters, Phys. Rev. Lett. 70, 1895(1993).

    Google Scholar 

  4. A. Ekert, Phys. Rev. Lett. 67, 661(1991).

    Google Scholar 

  5. I. Cirac and N. Gisin, Phys. Lett. A 229, 1(1997).

    Google Scholar 

  6. C. A. Fuchs, N. Gisin, R. B. Griffiths, C.-S. Niu, and A. Peres, Phys. Rev. A 56, 1163(1997).

    Google Scholar 

  7. S. L. Braunstein, C. M. Caves, R. Jozsa, N. Linden, S. Popescu, and R. Schack, Phys. Rev. Lett. 83, 1054(1999).

    Google Scholar 

  8. A. Ekert and R. Jozsa, Philos. Trans. R. Soc., London Ser. A 356, 1769(1998).

    Google Scholar 

  9. C. H. Bennett and S. Wiesner, Phys. Rev. Lett. 69, 2881(1992).

    Google Scholar 

  10. J. Eisert, K. Jacobs, P. Papadopoulos, and M. B. Plenio, Phys. Rev. A 62, 052317(2000).

    Google Scholar 

  11. J. I. Cirac, A. Ekert, S. F. Huelga, and C. Macchiavello, Phys. Rev. A 59, 4249(1999).

    Google Scholar 

  12. A. Thapliyal, Phys. Rev. A 59, 3336(1999).

    Google Scholar 

  13. J. Kempe, Phys. Rev. A 60, 910(1999).

    Google Scholar 

  14. C. H. Bennett, D. P. DiVincenzo, T. Mor, P. W. Shor, J. A. Smolin, and B. M. Terhal, Phys. Rev. Lett. 83, 3081(1999).

    Google Scholar 

  15. W. Dur, J. I. Cirac, and R. Tarrach, Phys. Rev. Lett. 83, 3562(1999).

    Google Scholar 

  16. D. P. DiVincenzo, T. Mor, P. W. Shor, J. A. Smolin, and B. M. Terhal, Comm. Math. Phys. 238, 379(2003).

    Google Scholar 

  17. J. A. Smolin, Phys. Rev. A 63, 032306(2001).

    Google Scholar 

  18. W. Dur and J. I. Cirac, Phys. Rev. A 62, 022302(2000).

    Google Scholar 

  19. P. W. Shor, J. A. Smolin and A. V. Thapliyal, Phys. Rev. Lett. 90, 107901(2003).

    Google Scholar 

  20. A. Wong and N. Christensen, Phys. Rev. A 63, 044301(2001).

    Google Scholar 

  21. D. J. Wineland, J. J. Bollinger, W. M. Itano, F. L. Moore, and D. J. Heinzen, Phys. Rev. A 46 R6797(1992)

    Google Scholar 

  22. A. Kuzmich, K. Mølmer and E. S. Polzik, Phys. Rev. Lett. 79, 4782(1997).

    Google Scholar 

  23. A. Kuzmich, N. P. Bigelow, and L. Mandel, Europhys. Lett. 42, 481(1998).

    Google Scholar 

  24. E. S. Polzik, Phys. Rev. A 59, 4202(1999).

    Google Scholar 

  25. J. Hald, J. L. Sørensen, C. Schori, and E. S. Polzik, Phys. Rev. Lett. 83, 1319(1999).

    Google Scholar 

  26. A. Kuzmich, L. Mandel, and N. P. Bigelow, Phys. Rev. Lett. 85, 1594(2000).

    Google Scholar 

  27. L.-M. Duan, J. I. Cirac, P. Zoller, and E. S. Polzik, Phys. Rev. Lett. 85, 5643(2000).

    Google Scholar 

  28. A. Kozhenkin, K. Mølmer, and E. S. Polzik, Phys. Rev. A 62, 033809(2000).

    Google Scholar 

  29. A. Sørensen, L.-M. Duan, J. I. Cirac, and P. Zoller, Nature (London), 409, 63(2001).

    Google Scholar 

  30. M. Kitagawa and M. Ueda, Phys. Rev. A 47, 5138(1993).

    Google Scholar 

  31. M. D. Lukin, S. F. Yelin, and M. Fleischhauer, Phys. Rev. Lett. 84, 4232(2000); A. Andre and M. D. Lukin, Phys. Rev. A 65, 053819(2002).

    Google Scholar 

  32. L. Vernac, M. Pinard, and E. Giacobino, Phys. Rev. A 62, 063812(2000).

    Google Scholar 

  33. K. Helmerson and L. You, Phys. Rev. Lett. 87, 170402(2001); Ö. E. Mustecapliolu, M. Zhang, and L. You, Phys. Rev. A 66, 033611(2002); S. Yi, O. E. Mustecapliolu, C. P. Sun, and L. You, Phys. Rev. A 66, 011601(2002); Ö. E. Mustecapliolu, M. Zhang, and L. You, Phys. Rev. A 66, 033611(2002).

    Google Scholar 

  34. C. Orzel, A. K. Tuchman, M. L. Fenselau, M. Yasuda, and M. A. Kasevich, Science 291, 2386(2001).

    Google Scholar 

  35. U. Poulsen and K. Mølmer, Phys. Rev. A 64, 013616(2001)

    Google Scholar 

  36. D. W. Berry and B. C. Sanders, New J. Phys. 4, 8(2002).

    Google Scholar 

  37. L. K. Thomsen, S. Mancini, and H. M. Wiseman, Phys. Rev. A 65, 061801(2002); D. W. Berry and B. C. Sanders, Phys. Rev. A 66, 012313(2002).

    Google Scholar 

  38. A. R. Usha Devi, K. S. Mallesh, M. A. A. Sbaih, K. B. Nalini, and G. Ramachandran, J. Phys. A: Math. Gen. 36, 5333(2003).

    Google Scholar 

  39. T. Gasenzer, D. C. Roberts, and K. Burnett, Phys. Rev. A 65, 021605(2002).

    Google Scholar 

  40. J. K. Stockton, J. M. Geremia, A. C. Doherty, and H. Mabuchi, Phys. Rev. A 67, 022112(2003).

    Google Scholar 

  41. Z. Ficek and R. Tanas, Phys. Rep. 372, 369(2002).

    Google Scholar 

  42. L. Zhou, H. S. Song and C. Li, J. Opt. B: Quantum Semiclass. Opt. 4, 425(2002).

    Google Scholar 

  43. X. Wang, A. Sørensen, and K. Mølmer, Phys. Rev. A 64, 053815(2001); X. Wang, J. Opt. B: Quantum Semiclassical Opt. 3, 93(2001); X. Wang, Opt. Commun. 200, 277(2001).

    Google Scholar 

  44. A. Sørensen, K. Mølmer, Phys. Rev. Lett. 86, 4431(2001).

    Google Scholar 

  45. K. Wodkiewicz and J. H. Eberly, J. Opt. Soc. Am. B 2, 458(1985).

    Google Scholar 

  46. G. S. Agarwal and R. R. Puri, Phys. Rev. A 41, 3782(1990); G. S. Agarwal and R. R. Puri, Phys. Rev. A 41, 4968(1994).

    Google Scholar 

  47. D. J. Wineland, J. J. Bollinger, W. M. Itano and D. J. Heinzen, Phys. Rev. A 50, 67(1994).

    Google Scholar 

  48. B. Yurke, Phys. Rev. Lett. 56, 1515(1986); M. Kitagawa and M. Ueda, Phys. Rev. Lett. 67, 1852(1991).

    Google Scholar 

  49. R. Horodecki and M. Horodecki, Phys. Rev. A 54, 1838(1996).

    Google Scholar 

  50. L. C. Biedenharn and J. D. Louck, Angular Momentum in Quantum Physics (Addison-Wesley Publishing Company, 1981).

  51. D. Ulam-Orgikh and M. Kitagawa, Phys. Rev. A 64, 052106(2001).

    Google Scholar 

  52. D. W. Berry and B. C. Sanders, New J. Phys. 4, 8(2002).

    Google Scholar 

  53. M. G. Raymer, A. C. Funk, B. C. Sanders, and H. de Guise, Phys. Rev. A 67, 052104(2003).

    Google Scholar 

  54. X. Wang and B. C. Sanders, Phys. Rev. A 68, 03382(2003); X. Wang and K. Mølmer, Eur. Phys. J. D 18, 385(2002).

    Google Scholar 

  55. S. Hill and, W. K. Wootters, Phys. Rev. Lett. 78, 5022(1997); W. K. Wootters, Phys. Rev. Lett. 80, 2245(1998).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to B.C. Sanders.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Usha Devi, A., Wang, X. & Sanders, B. Spin Squeezing Criterion with Local Unitary Invariance. Quantum Information Processing 2, 207–220 (2003). https://doi.org/10.1023/B:QINP.0000004125.12489.f4

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:QINP.0000004125.12489.f4

Navigation