Quantum Information Processing

, Volume 12, Issue 4, pp 1627–1636 | Cite as

Entanglement dynamics of two-qubit pure state

  • Jun Zhang


We show that the entanglement dynamics for the pure state of a closed two-qubit system is part of a 10-dimensional complex linear differential equation defined on a supersphere, and the coefficients therein are completely determined by the system Hamiltonian. We apply the result to two physical examples of Josephson junction qubits and exchange Hamiltonians, deriving analytic solutions for the time evolution of entanglement. The Hamiltonian coefficients determine whether the entanglement is periodic. These results allow of investigating how to generate and manipulate entanglements efficiently, which are required by both quantum computation and quantum communication.


Quantum entanglement Entanglement dynamics Two-qubit system Dynamical equation 


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  1. 1.
    Nielsen M., Chuang I.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge, UK (2000)zbMATHGoogle Scholar
  2. 2.
    Horodecki R., Horodecki P., Horodecki M., Horodecki K.: Quantum entanglement. Rev. Mod. Phys. 81(2), 865–942 (2009)MathSciNetADSzbMATHCrossRefGoogle Scholar
  3. 3.
    Mintert F., Carvalho A., Kus M., Buchleitner A.: Measures and dynamics of entangled states. Phys. Rep. 415(4), 207–259 (2005)MathSciNetADSCrossRefGoogle Scholar
  4. 4.
    Yu T., Eberly J.H.: Finite-time disentanglement via spontaneous emission. Phys. Rev. Lett. 93, 140–404 (2004)Google Scholar
  5. 5.
    Yu T., Eberly J.H.: Quantum open system theory: bipartite aspects. Phys. Rev. Lett. 97, 140,403 (2006)Google Scholar
  6. 6.
    Yu T., Eberly J.H.: Sudden death of entanglement. Science 323(5914), 598–601 (2009)MathSciNetADSzbMATHCrossRefGoogle Scholar
  7. 7.
    Konrad T., De Melo F., Tiersch M., Kasztelan C., Aragao A., Buchleitner A.: Evolution equation for quantum entanglement. Nat. Phys. 4(2), 99–102 (2008)CrossRefGoogle Scholar
  8. 8.
    An J.H., Wang S.J., Luo H.G.: Entanglement dynamics of qubits in a common environment. Physica A 382, 753–764 (2007)ADSCrossRefGoogle Scholar
  9. 9.
    Cui H.T., Li K., Yi X.X.: A study on the suddent death of entanglement. Phys. Lett. A 365, 44–48 (2007)MathSciNetADSzbMATHCrossRefGoogle Scholar
  10. 10.
    Życzkowski K, Z K., Horodecki P., Horodecki M., Horodecki R.: Dynamics of quantum entanglement. Phys. Rev. A 65(1), 012–101 (2001)Google Scholar
  11. 11.
    Dodd P.J., Halliwell J.J.: Disentanglement and decoherence by open system dynamics. Phys. Rev. A 69(5), 052–105 (2004)MathSciNetGoogle Scholar
  12. 12.
    Dür W., Briegel H.J.: Stability of macroscopic entanglement under decoherence. Phys. Rev. Lett. 92(18), 180–403 (2004)CrossRefGoogle Scholar
  13. 13.
    Santos M.F., Milman P., Davidovich L., Zagury N.: Direct measurement of finite-time disentanglement induced by a reservoir. Phys. Rev. A 73(4), 040–305 (2006)CrossRefGoogle Scholar
  14. 14.
    Carvalho A.R.R., Busse M., Brodier O., Viviescas C., Buchleitner A.: Optimal dynamical characterization of entanglement. Phys. Rev. Lett. 98(19), 190–501 (2007)CrossRefGoogle Scholar
  15. 15.
    Roos C.: Dynamics of entanglement. Nat. Phys. 4(2), 97–98 (2008)CrossRefGoogle Scholar
  16. 16.
    Roszak K., Machnikowski P.: Complete disentanglement by partial pure dephasing. Phys. Rev. A 73, 022–313 (2006)Google Scholar
  17. 17.
    Ficek Z., Tanaś R.: Dark periods and revivals of entanglement in a two-qubit system. Phys. Rev. A 74, 024–304 (2006)CrossRefGoogle Scholar
  18. 18.
    Liu R.F., Chen C.C.: Role of the bell singlet state in the suppression of disentanglement. Phys. Rev. A 74, 024–102 (2006)Google Scholar
  19. 19.
    Zhang J., Vala J., Sastry S., Whaley K.B.: Geometric theory of nonlocal two-qubit operations. Phys. Rev. A 67, 042–313 (2003)MathSciNetGoogle Scholar
  20. 20.
    Wootters W.K.: Entanglement of formation of an arbitrary state of two qubits. Phys. Rev. Lett. 80, 2245 (1998)ADSCrossRefGoogle Scholar
  21. 21.
    Makhlin Y.: Nonlocal properties of two-qubit gates and mixed states and the optimization of quantum computations. Quantum Inf. Process. 1(4), 243–252 (2002)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Makhlin Y., Schön G., Shnirman A.: Josephson-junction qubits with controlled couplings. Nature 398, 305 (1999)ADSCrossRefGoogle Scholar

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© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Joint Institute of UMich-SJTUShanghai Jiao Tong UniversityShanghaiChina
  2. 2.Key Laboratory of System Control and Information ProcessingMinistry of EducationShanghaiChina

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