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Concurrence for a two-qubits mixed state consisting of three pure states in the framework of SU(2) coherent states

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Abstract

A simplified expression of concurrence for two-qubit mixed state having no more than three non-vanishing eigenvalues is obtained. Basing on SU(2) coherent states, the amount of entanglement of two-qubit pure states is studied and conditions for entanglement are calculated by formulating the measure in terms of some new parameters (amplitudes of coherent states). This formalism is generalized to the case of two-qubit mixed states using the simplified expression of concurrence.

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References

  1. Bennett C.H., Brassard G., Crepeau C., Jozsa R., Peres A., Wootters W.K.: Teleporting an unknown quantum state via dual classical and Einstein Podolsky Rosen channels. Phys. Rev. Lett. 70, 1895–1899 (1993)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  2. Bouwmeester D., Pan J.W., Mattle K., Eibl M., Weinfurter H., Zeilinger A.: Experimental quantum teleportation. Nature 390, 575–579 (1997)

    Article  ADS  Google Scholar 

  3. Bennet, C.H., Brassard, G., Quantum cryptography: public key distribution and coin tossing. In: Proceedings of IEEE International Conference on Computers, Systems and Signal Processing. pp. 175–179 (1984)

  4. Ekert A.K.: Quantum cryptography based on Bell’s theorem. Phys. Rev. Lett. 67, 661–663 (1991)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  5. Bennett C.H., Wiesner S.J.: Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states. Phys. Rev. Lett. 69, 2881 (1992)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  6. Braunstein S.L., Kimble H.J.: Dense coding for continuous variables. Phys. Rev. A 61, 042302 (2000)

    Article  MathSciNet  ADS  Google Scholar 

  7. Mattle K., Weinfurter H., Kwait P.G., Zeilinger A.: Dense coding in experimental quantum communication. Phys. Rev. Lett. 76, 4656 (1996)

    Article  ADS  Google Scholar 

  8. Nielsen M.A., Chuang I.L.: Quantum Computation and Information. Cambridge university press, Cambridge, UK (2000)

    MATH  Google Scholar 

  9. Barenco A., Deutsch D., Ekert A., Jozsa R.: Conditional quantum dynamics and quantum gates. Phys. Rev. Lett. 74, 4083–4086 (1995)

    Article  ADS  Google Scholar 

  10. Deutsch D.: Quantum computational networks. Proc. R. Soc. Lond. A 425, 73–90 (1985)

    MathSciNet  ADS  Google Scholar 

  11. Mintert F., Kuś M., Buchleitner A.: Concurrence of mixed multipartite quantum states. Phys. Rev. Lett. 95, 260502–260506 (2005)

    Article  MathSciNet  ADS  Google Scholar 

  12. Mintert F., Buchleitner A.: Observable entanglement measure for mixed quantum states. Phys. Rev. Lett. 98, 140505 (2007)

    Article  MathSciNet  ADS  Google Scholar 

  13. Aolita L., Buchleitner A., Mintert F.: Scalable method to estimate experimentally the entanglement of multipartite systems. Phys. Rev. A 78, 022308 (2008)

    Article  ADS  Google Scholar 

  14. Bennett C.H., Bernstein H.J., Popescu S., Schumacher B.: Concentrating partial entanglement by local operations. Phys. Rev. A 53, 2046–2052 (1996)

    Article  ADS  Google Scholar 

  15. Rungta P., Buzek V., Caves C.M., Hillery M., Milburn G.J.: Universal state inversion and concurrence in arbitrary dimensions. Phys. Rev. A 64, 042315 (2001)

    Article  MathSciNet  ADS  Google Scholar 

  16. Kuang L.M., Zhou L.: Generation of atom-photon entangled states in atomic Bose-Einstein condensate via electromagnetically induced transparency. Phys. Rev. A 68, 043606 (2003)

    Article  ADS  Google Scholar 

  17. Uhlmann A.: Fidelity and concurrence of conjugated states. Phys. Rev. A 62, 032307 (2000)

    Article  MathSciNet  ADS  Google Scholar 

  18. Peres A.: Separability criterion for density matrices. Phys. Rev. Lett. 77, 1413–1415 (1996)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  19. Horodecki M., Horodecki P., Horodecki R.: Separability of mixed states: necessary and sufficient conditions. Phys. Lett. A 223, 1–8 (1996)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  20. Vidal G., Werner R.F.: Computable measure of entanglement. Phys. Rev. A 65, 032314 (2002)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  22. Wong A., Christensen N.: Potential multiparticle entanglement measure. Phys. Rev. A 63, 044301 (2001)

    Article  ADS  Google Scholar 

  23. Osborne T.J., Verstraete F.: General monogamy inequality for bipartite qubit entanglement. Phys. Rev. Lett. 96, 220503 (2006)

    Article  ADS  Google Scholar 

  24. Terhal B.M., Vollbrecht K.G.H.: Entanglement of formation for isotropic states. Phys. Rev. Lett. A 85, 2625–2628 (2000)

    Article  ADS  Google Scholar 

  25. Rungta P., Caves C.M.: Concurrence-based entanglement measures for isotropic states. Phys. Rev. A 67, 012307 (2003)

    Article  ADS  Google Scholar 

  26. Hill S., Wootters W.K.: Entanglement of a pair of quantum bits. Phys. Rev. Lett. 78, 5022–5025 (1997)

    Article  ADS  Google Scholar 

  27. Schrödinger E.: The continuous transition from micro-to macro-mechanics. Naturwissenschafter 14, 664 (1926)

    Article  ADS  Google Scholar 

  28. Klauder J.R., Skagerstam B.-S.: Coherent states-applications in physics and mathematical physics. World Scientific, Singapore (1985)

    MATH  Google Scholar 

  29. Mandel L., Wolf E.: Optical Coherence and Quantum Optics. Cambridge University Press, Cambridge (1995)

    Google Scholar 

  30. Eleuch H., Bennaceur R.: Quantum semiclass. J. Opt. B 6, 189–195 (2004)

    Article  ADS  Google Scholar 

  31. Ralph T.C.: Quantum optical systems for implementation of quantum information processes. Rep. Prog. Phys. 69, 853–898 (2006)

    Article  ADS  Google Scholar 

  32. Lloyd S., Braunstein S.L.: Quantum computation over continuous variables. Phys. Rev. Lett. 82, 1784–1787 (1999)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  33. Perelomov A.: Generalized Coherent States and Their Applications. Springer, Berlin (1986)

    MATH  Google Scholar 

  34. Funahashi K., Kashiwa T., Sakoda S., Fujii K.: Coherent states, path integral, and semiclassical approximation. J. Math. Phys. 36, 3232–3253 (1995)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  35. Funahashi K., Kashiwa T., Sakoda S., Fujii K.: Exactness in the WKB approximation for some homogeneous spaces. J. Math. Phys. 36, 4590–4611 (1995)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  36. Fujii K., Kashiwa T., Sakoda S.: Coherent states over Grassmann manifolds and the WKB-exactness in path integral. J. Math. Phys. 37, 567–602 (1996)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  37. Dömötör P., Benedict M.G.: Coherent states and global entanglement in an N qubit system. Phys. Lett. A 372, 3792–3795 (2008)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  38. Berrada K., Chafik A., Eleuch H., Hassouni Y.: Concurrence in the framework of coherent states. Quantum Inf. Process. 9, 13–26 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  39. Berrada K., El Baz M., Eleuch H., Hassouni Y.: A comparative study of negativity and concurrence based on spin coherent states. Int. J. Mod. Phys. C 21, 291–305 (2010)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  40. Di Y.M., Hu B.L., Liu D.D. et al.: Concurrence of the mixed state of two non-orthogonal pure states. Acta. Phys. Sin. 55, 3869–3874 (2006)

    Google Scholar 

  41. Berrada K., Chafik A., Eleuch H., Hassouni Y.: Entanglement of two-qubit nonorthogonal states. Int. J. Mod. Phys. B 23, 2021–2027 (2009)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  42. Katriel J., Solomon A.I.: Nonideal lasers, nonclassical light, and deformed photon states. Phys. Rev. A 49, 5149–5151 (1994)

    Article  ADS  Google Scholar 

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Salimi, S., Mohammadzade, A. & Berrada, K. Concurrence for a two-qubits mixed state consisting of three pure states in the framework of SU(2) coherent states. Quantum Inf Process 11, 501–518 (2012). https://doi.org/10.1007/s11128-011-0260-z

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  • DOI: https://doi.org/10.1007/s11128-011-0260-z

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