Skip to main content
SpringerLink
Log in

A useful strong lower bound on two-qubit concurrence

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

A new strong lower bound on concurrence for two-qubit states is derived. Its equality with the concurrence itself for the pure- and X-states is proved analytically; while extensive numerical computations show that equality for a general mixed state may also exist. Being a very simple function and easy to calculate, it is more convenient and practical than the exact value in some cases, including entanglement investigations in spin chains. We study thermal localizable entanglement in spin chains as an example, to demonstrate the convenience of this bound.

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.

Similar content being viewed by others

References

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

    Article  ADS  MathSciNet  MATH  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  3. 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  ADS  MathSciNet  MATH  Google Scholar 

  4. Bennett C.H., Brassard G., Mermin N.D.: Quantum cryptography without Bell’s theorem. Phys. Rev. Lett. 68, 557 (1992)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  5. 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 (1993)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  6. Di Vincenzo D.P.: Quantum computation. Science 270, 255 (1995)

    Article  ADS  MathSciNet  Google Scholar 

  7. Deutsch D., Ekert A., Jozsa R., Macchiavello C., Popescu S., Sanpera A.: Quantum privacy amplification and the security of quantum cryptography over noisy channels. Phys. Rev. Lett. 77, 2818 (1996)

    Article  ADS  Google Scholar 

  8. 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 

  9. Vedral V., Plenio M.B., Rippen M.A., Knight P.L.: Quantifying entanglement. Phys. Rev. Lett. 78, 2275 (1997)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  10. Shor P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. Siam J. Comput. 26, 1484 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  11. Grover L.K.: Quantum mechanics helps in searching for a needle in a haystack. Phys. Rev. Lett. 79, 325 (1997)

    Article  ADS  Google Scholar 

  12. Rains E.M.: Rigorous treatment of distillable entanglement. Phys. Rev. A 60, 173 (1999)

    Article  ADS  Google Scholar 

  13. Bennett C.H., Di Vincenzo D.P., Smolin J., Wootters W.K.: Mixed-state entanglement and quantum error correction. Phys. Rev. A 54, 3824 (1996)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  14. Hill S., Wootters W.K.: Entanglement of a pair of quantum bits. Phy. Rev. Lett. 78, 5022 (1997)

    Article  ADS  Google Scholar 

  15. Wootters W.K.: Entanglement of formation of an arbitrary state of two qubits. Phys. Rev. Lett. 80, 2245 (1998)

    Article  ADS  MATH  Google Scholar 

  16. Jafarpour M., Akhound A.: Entanglement and squeezing of multi-qubit systems using a two-axis countertwisting Hamiltonian with an external fild. Phys. Lett. A 372, 2374 (2008)

    Article  ADS  MATH  Google Scholar 

  17. Gonzalez-H C.T., Franco R., Silva-Valencia J.: Concurrence of finite Ising chains with the Dzyaloshinsky-Moriya interaction. Eur. J. Phys. 31, 681 (2010)

    Article  MATH  Google Scholar 

  18. Sabour A., Jafarpor M.: A probability measure for entanglement of pure two-qubit systems and a useful interpretation for concurrence. Chin. Phys. Lett. 28, 070301 (2011)

    Article  Google Scholar 

  19. Yu T., Eberly J.H.: Evolution from entanglement to decoherence of bipartite mixed “X” states. Quantum Inf. Comput. 7, 459 (2007)

    MathSciNet  MATH  Google Scholar 

  20. Ban M.: Entanglement, phase correlation and dephasing of two-qubit states. Optics Commun. 281, 3943 (2008)

    Article  ADS  Google Scholar 

  21. Kiefer, C., Joos, E.: Decoherence: concepts and examples. quant-ph/9803052

  22. Uhlmann A.: Entropy and optimal decompositions of states relative to a maximal commutative subalgebra. Open Syst. Inf. Dyn. 5, 209 (1998)

    Article  MATH  Google Scholar 

  23. Horodecki M.: Entanglement measures. Quantum Inf. Comput. 1, 3 (2001)

    MathSciNet  MATH  Google Scholar 

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

    Article  ADS  MathSciNet  MATH  Google Scholar 

  25. Verstraete F., Popp M., Cirac J.I.: Entanglement versus correlations in spin systems. Phys. Rev. Lett. 92, 027901 (2004)

    Article  ADS  Google Scholar 

  26. Jin B.-Q., Korepin V.E.: Localizable entanglement in antiferromagnetic spin chains. Phys. Rev. A 69, 062314 (2004)

    Article  ADS  Google Scholar 

  27. Subrahmanyam V., Lakshminarayan A.: Transport of entanglement through a Heisenberg–XY spin chain. Phys. Lett. A 349, 164 (2006)

    Article  ADS  Google Scholar 

  28. Popp M., Verstraete F., Martin-Delgado M.A., Cirac J.I.: Localizable entanglement. Phys. Rev. A 71, 042306 (2005)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  29. Popp M., Verstraete F., Martin-Delgado M.A., Cirac J.I.: Numerical computation of localizable entanglement in spin chains. Appl. Phys. B 82, 225 (2006)

    Article  ADS  Google Scholar 

  30. Teresi D., Napoli A., Messina A.: Thermal localizable entanglement in a simple multipartite system. Phys. Scr. T 135, 014038 (2009)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  32. Wang X.: Entanglement in the quantum Heisenberg XY model. Phy. Rev. A 64, 012313 (2001)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Physics Department, Shahid Chamran University, Ahvaz, Iran

    Mojtaba Jafarpour & Abbass Sabour

Authors
  1. Mojtaba Jafarpour
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Abbass Sabour
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mojtaba Jafarpour.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jafarpour, M., Sabour, A. A useful strong lower bound on two-qubit concurrence. Quantum Inf Process 11, 1389–1402 (2012). https://doi.org/10.1007/s11128-011-0288-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11128-011-0288-0

Keywords

Search

Navigation