Skip to main content
SpringerLink
Log in

Entanglement of Multi-qudit States Constructed by Linearly Independent Coherent States: Balanced Case

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

Abstract

Multi-mode entangled coherent states are important resources for linear optics quantum computation and teleportation. Here we introduce the generalized balanced N-mode coherent states which recast in the multi-qudit case. The necessary and sufficient condition for bi-separability of such balanced N-mode coherent states is found. We particularly focus on pure and mixed multi-qubit and multi-qutrit like states and examine the degree of bipartite as well as tripartite entanglement using the concurrence measure. Unlike the N-qubit case, it is shown that there are qutrit states violating monogamy inequality. Using parity, displacement operator and beam splitters, we will propose a scheme for generating balanced N-mode entangled coherent states for even number of terms in superposition.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

References

  1. Schrödinger, E.: Naturwissenschaften 14, 664 (1926)

    Article  ADS  MATH  Google Scholar 

  2. Einstein, A., Podolski, B., Rosen, N.: Phys. Rev. 47, 777–780 (1935)

    Article  ADS  MATH  Google Scholar 

  3. Cochrane, P.T., Milburn, G.J., Munro, W.J.: Phys. Rev. A 59, 2631 (1999)

    Article  ADS  Google Scholar 

  4. De Oliveira, M.C., Munro, W.J.: Phys. Rev. A 61, 042309 (2000)

    Article  ADS  Google Scholar 

  5. Jeong, H., Kim, M.S.: Phys. Rev. A 65, 042305 (2002)

    Article  ADS  Google Scholar 

  6. Sanders, B.C.: Phys. Rev. A 45(9) (1992)

  7. Ralph, T.C., Gilchrist, A., Milburn, G.J.: Phys. Rev. A 68, 042319 (2003)

    Article  ADS  Google Scholar 

  8. Munro, W.J., Milburn, G.J., Sanders, B.C.: Phys. Rev. A 62, 052108 (2001)

    Article  ADS  Google Scholar 

  9. Wang, X.: Phys. Rev. A 64, 022302 (2001)

    Article  ADS  MathSciNet  Google Scholar 

  10. Van Enk, S.J., Hirota, O.: Phys. Rev A 67, 022313 (2001)

    Article  ADS  Google Scholar 

  11. Wang, X., Sanders, B.C., Pan, S.H.: J. Phys. A 33, 7451 (2000)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  12. Vogel, W., Sperling, J.: Phys. Rev. A 89, 052302 (2014)

    Article  ADS  Google Scholar 

  13. El Allati, A., Hassouni, Y., Metwally, N.: Phys. Scr. 83, 065002 (2011)

    Article  ADS  Google Scholar 

  14. Cheong, Y.W., Lee, J.: J. Korean Phys. Soc. 51, 4 (2007)

    Article  Google Scholar 

  15. van Enk, S.J.: Phys. Rev. Lett. 91, 1 (2003)

    Article  Google Scholar 

  16. Wang, X., Sanders, B.C.: Phys. Rev. A 65, 012303 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  17. Wang, X., Phys, J.: J. Phys. A, Math. Gen. 35(1), 165–173 (2002)

    Article  ADS  MATH  Google Scholar 

  18. Fu, H., Wang, X., Solomon, A.I.: Phys. Lett. A 291, 73–76 (2001)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  19. Najarbashi, G., Maleki, Y.: International Journal Theoretical Physical (2011)

  20. Daoud, M., Choubabi, E.B.: Int. J. Quantum Inf. 10, 1 (2012)

    MathSciNet  Google Scholar 

  21. Daoud, M., Ahl Laamara, R., Essaber, R., Kaydi, W.: Phys. Scr. 89, 065004 (2014)

    Article  ADS  Google Scholar 

  22. Wootters, W.K.: Phys. Rev. Lett. 80, 2245 (1998)

    Article  ADS  Google Scholar 

  23. Wootters, W.K.: Quantum Inf. Comput. 1, 1 (2001)

    MathSciNet  Google Scholar 

  24. Akhtarshenas, S.J.: J. Phys. A: Math. Gen. 38, 6777–6784 (2005)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  25. Coffman, V., Kundu, J., Wootters, W.K.: Phys. Rev. A 61, 052306 (2000)

    Article  ADS  Google Scholar 

  26. Kim, J.S., Das, A., Sanders, B.C.: Phys. Rev. A 79, 012329 (2009)

    Article  ADS  Google Scholar 

  27. Sanders, B.C., J.S. Kim: Appl. Math. Inf. Sci. 4(3) (2010)

  28. Li, Y.Q., Zhu, G.Q.: Front. Phys. China 3(3), 250–257 (2008)

    Article  ADS  Google Scholar 

  29. Sanders, B.C.: J. Phys. A: Math. Theor. 45 (2012)

  30. Milburn, G.J.: Phys. Rev. A 33(1) (1986)

  31. Milburn, G.J., Holmes, C.: Phys. Rev. Lett. 56(21) (1986)

  32. Yurke, B., Stoler, D.: Phys. Rev. Lett. 57(1) (1986)

  33. Yurke, B., Stoler, D.: Phys. Rev. A 35(11) (1987)

  34. Messina, A., Militello B., Napoli, A.: Proceedings of Institute of Mathematics of NAS of Ukraine, Vol. 50, Part 2 (2004)

  35. Messina, A., Draganescu, G. Preprint, arxiv:quant-ph/1306.2524v2 (2013)

  36. Paprzycka, M., Tanas, R.: Quantum opt. 4 (1992)

  37. Miranowicz, A., Tanas, R., Kielich, S.: Quantum opt. 2, 253 (1990)

    Article  ADS  Google Scholar 

  38. Gantsog, Ts., Tanas, R.: Quantum opt. 3, 33 (1991)

    Article  ADS  Google Scholar 

Download references

Acknowledgments

The authors also acknowledge the support from the University of Mohaghegh Ardabili.

Author information

Authors and Affiliations

  1. Department of Physics, University of Mohaghegh Ardabili, P.O. Box 179, Ardabil, Iran

    G. Najarbashi & S. Mirzaei

Authors
  1. G. Najarbashi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. Mirzaei
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to G. Najarbashi.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Najarbashi, G., Mirzaei, S. Entanglement of Multi-qudit States Constructed by Linearly Independent Coherent States: Balanced Case. Int J Theor Phys 55, 1336–1353 (2016). https://doi.org/10.1007/s10773-015-2775-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10773-015-2775-z

Keywords

Search

Navigation