Skip to main content

Advertisement

Springer Nature Link
Log in

Beam splitting and entanglement generation: excited coherent states

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

We study the mathematical properties of the excited coherent states, which are obtained through actions of a photon creation operator of the mode optical field on its corresponding coherent state, by analyzing the minimal set of Klauder’s coherent states. Using linear entropy as a measure of entanglement, we investigate in detail the entanglement generated via a beam splitter when an excited coherent state is injected on one input mode and vacuum state is injected on the other one. Finally, we examine the physical properties of the excited coherent states through the Mandel’s parameter and the Wehrl entropy and we give the correlation between these parameters and the entanglement of the output state.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Bell J.S.: On the Einstein–Podolsky–Rosen paradox. Physics 1, 195–200 (1964)

    Google Scholar 

  2. Einstein A., 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 

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

    MATH  Google Scholar 

  4. 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 

  5. Agrawal P., Pati A.: Perfect teleportation and superdense coding with W states. Phys. Rev. A 74, 062320 (2006)

    Article  ADS  Google Scholar 

  6. Yin Z.Q. et al.: Security of counterfactual quantum cryptography. Phys. Rev. A 82, 042335 (2010)

    Article  ADS  Google Scholar 

  7. Noh T.G.: Counterfactual quantum cryptography. Phys. Rev. Lett. 103, 230501 (2009)

    Article  MathSciNet  ADS  Google Scholar 

  8. Morimae T.: Strong entanglement causes low gate fidelity in inaccurate one-way quantum computation. Phys. Rev. A 81, 060307 (2010)

    Article  ADS  Google Scholar 

  9. Schaffry M. et al.: Quantum metrology with molecular ensembles. Phys. Rev. A 82, 042114 (2010)

    Article  ADS  Google Scholar 

  10. Wootters W.K.: Entanglement of formation and concurrence. Quantum Inf. Comput. 1, 27 (2001)

    MathSciNet  MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

  12. Popescu S., Rohrlich D.: Thermodynamics and the measure of entanglement. Phys. Rev. A 56, R3319 (1997)

    Article  MathSciNet  ADS  Google Scholar 

  13. Zyczkowski K., Horodecki P., Sanpera A., Lewenstein M.: Volume of the set of separable states. Phys. Rev. A 58, 883 (1998)

    Article  MathSciNet  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  15. Berrada K., El Baz M., Saif F., Hassouni Y., Mnia S.: Entanglement generation from deformed spin coherent states using a beam splitter. J. Phys. A Math. Theor. 42, 285306 (2009)

    Article  MathSciNet  Google Scholar 

  16. Gerry C.C., Benmoussa A.: Beam splitting and entanglement: generalized coherent states, group contraction, and the classical limit. Phys. Rev. A 71, 062319 (2005)

    Article  ADS  Google Scholar 

  17. Tan S.M., Walls D.F., Collett M.J.: Nonlocality of a single photon. Phys. Rev. Lett. 66, 252–255 (1991)

    Article  ADS  Google Scholar 

  18. Sanders B.C.: Entangled coherent states. Phys. Rev. A 45, 6811–6815 (1992)

    Article  ADS  Google Scholar 

  19. Sanders B.C., Lee K.S., Kim M.S.: Optical homodyne measurements and entangled coherent states. Phys. Rev. A 52, 735–741 (1995)

    Article  ADS  Google Scholar 

  20. Toth G., Simon C., Cirac J.I.: Entanglement detection based on interference and particle counting. Phys. Rev. A 68, 062310 (2003)

    Article  ADS  Google Scholar 

  21. Kim M.S., Son W., Buzek V., Knight P.L.: Entanglement by a beam splitter: nonclassicality as a prerequisite for entanglement. Phys. Rev. A 65, 032323 (2002)

    Article  ADS  Google Scholar 

  22. Rauschenbeutel A., Nogues G., Osnaghi S., Bertet P., Brune M., Raimond J.M., Haroche S.: Step-by-step engineered multiparticle entanglement. Science 288, 2024 (2000)

    Article  ADS  Google Scholar 

  23. Zheng S.-B., Guo G.-C.: Efficient scheme for two-atom entanglement and quantum information processing in cavity QED. Phys. Rev. Lett. 85, 2392–2395 (2000)

    Article  ADS  Google Scholar 

  24. Zhang J.S., Chen A.X., Abdel-Aty M.: Two atoms in dissipative cavities in dispersive limit: entanglement sudden death and long-lived entanglement. J. Phys. B At. Mol. Opt. Phys. 43, 025501 (2010)

    Article  ADS  Google Scholar 

  25. Gershenfeld N., Chuang I.L.: Bulk spin-resonance quantum computation. Science 275, 350–356 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  26. Braunstein L., Caves C.M., Jozsa R., Linden N., Popescu S., Schack R.: Separability of very noisy mixed states and implications for NMR quantum computing. Phys. Rev. Lett. 83, 1054–1057 (1999)

    Article  ADS  Google Scholar 

  27. Ivan, J.S., Mukunda, N., Simon, R.: Generation of NPT Entanglement from Nonclassical Photon Statistics. Quant-Ph/0603255

  28. Berrada K., El Baz M., Hassouni Y.: Generalized spin coherent states: construction and some physical properties. J. Stat. Phys. 142, 510 (2011)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  29. Berrada K., Hassouni Y.: Maximal entanglement of bipartite spin states in the context of quantum algebra. Eur. Phys. J. D 61, 513 (2011)

    Article  ADS  Google Scholar 

  30. Berrada K., El Baz M., Hassouni Y.: Generalized Heisenberg algebra coherent states for power-law potentials. Phys. Lett. A 375, 298 (2011)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  31. Eleuch H.: Photon statistics of light in semiconductor microcavities. J. Phys. B 41, 055502 (2008)

    Article  ADS  Google Scholar 

  32. Hassouni Y., Curado E.M.F., Rego-Monteiro M.A.: Construction of coherent states for physical algebraic systems. Phys. Rev. A 71, 022104 (2005)

    Article  MathSciNet  ADS  Google Scholar 

  33. Eleuch H., Rachid N.: Autocorrelation function of microcavity-emitting field in the non-linear regime. Eur. Phys. J. D 57, 259 (2010)

    Article  ADS  Google Scholar 

  34. Eleuch H., Bennaceur R.: Nonlinear dissipation and the quantum noise of light in semiconductor microcavities. J. Opt. B Quantum Semiclassical Opt. 6, 189 (2004)

    Article  ADS  Google Scholar 

  35. Glauber R.J.: Coherent and incoherent states of the radiation field. Phys. Rev. 131, 2766 (1963)

    Article  MathSciNet  ADS  Google Scholar 

  36. Perlomov A.M.: Coherent states for arbitrary Lie group. Commun. Math. Phys. 26, 222 (1972)

    Article  ADS  Google Scholar 

  37. Perelomov A.: Generalized Coherent States and Their Applications. Springer, New York (1986)

    Book  MATH  Google Scholar 

  38. Zhang W.M., Feng D.H., Gilmore R.: Coherent states, theory and some applications. Rev. Mod. Phys. 62, 867–927 (1990)

    Article  MathSciNet  ADS  Google Scholar 

  39. Inomata A., Kuratsuji H., Gerry C.: Path Integrals and Coherent States of SU(2) and SU(1,1). World Scientific, Singapore (1992)

    Google Scholar 

  40. Agarwal G.S., Tara K.: Nonclassical properties of states generated by the excitations on a coherent state. Phys. Rev. A 43, 492–497 (1991)

    Article  ADS  Google Scholar 

  41. Markham D., Vedral V.: Classicality of spin-coherent states via entanglement and distinguishability. Phys. Rev. A 67, 042113 (2003)

    Article  ADS  Google Scholar 

  42. Nielsen M.A.: Conditions for a class of entanglement transformations. Phys. Rev. Lett. 83, 436–439 (1999)

    Article  ADS  Google Scholar 

  43. Mandel L., Wolf E.: Optical Coherence and Quantum Optics. Cambridge University Press, Cambridge (1955)

    Google Scholar 

  44. Wehrl A.: On the relation between classical and quantum-mechanical entropy. Rep. Math. Phys. 16, 353–358 (1979)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  45. Short R., Mandel L.: Observation of sub-poissonian photon statistics. Phys. Rev. Lett. 51, 384–387 (1983)

    Article  ADS  Google Scholar 

  46. Perina J., Hradil Z., Jurco B.: Quantum Optics and Fundamentals of Physics. Kluwer, Dordrechet (1994)

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Abdus Salam International Centre for Theoretical Physics, ICTP, Trieste, Italy

    K. Berrada & S. Abdel-Khalek

  2. Mathematics Department, Faculty of Science, Sohag University, Sohag, 82524, Egypt

    S. Abdel-Khalek

  3. Laboratoire de Physique Théorique URAC 13, Faculté des Sciences, Université Mohammed V-Agdal, Av. Ibn Battouta, B.P. 1014, Agdal Rabat, Morocco

    K. Berrada & Y. Hassouni

  4. Department of Physics and Astronomy, Institute for Quantum Science and Engineering, Texas University, College Station, TX, 77843, USA

    H. Eleuch

Authors
  1. K. Berrada
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. Abdel-Khalek
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. H. Eleuch
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Y. Hassouni
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to K. Berrada.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Berrada, K., Abdel-Khalek, S., Eleuch, H. et al. Beam splitting and entanglement generation: excited coherent states. Quantum Inf Process 12, 69–82 (2013). https://doi.org/10.1007/s11128-011-0344-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11128-011-0344-9

Keywords