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Quantum Information Processing

, Volume 11, Issue 3, pp 841–851 | Cite as

Entangled brachistochrone: minimum time to reach the target entangled state

  • Arun Kumar Pati
  • Biswajit Pradhan
  • Pankaj Agrawal
Article

Abstract

We address the question: Given an arbitrary initial state and a general physical interaction what is the minimum time for reaching a target entangled state? We show that the minimum time is inversely proportional to the quantum mechanical uncertainty in the non-local Hamiltonian. We find that the presence of initial entanglement helps to minimize the waiting time. We bring out a connection between the entangled brachistochrone and the entanglement rate. Furthermore, we find that in a bi-local rotating frame the entangling capability is actually a geometric quantity. We give a bound for the time average of entanglement rate for general quantum systems which goes as \({{\bar \Gamma} \le 2 \log N \frac{\Delta H}{\hbar S_0}}\) . The time average of entanglement rate does not depend on the particular Hamiltonian, rather on the fluctuation in the Hamiltonian. There can be infinite number of nonlocal Hamiltonians which may give same average entanglement rate. We also prove a composition law for minimum time when the system evolves under a composite Hamiltonian.

Keywords

Quantum entanglement Geometric uncertainty relation Composite Hamiltonian Quantum computation 

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References

  1. 1.
    DiVincenzo D.P., Bennett C.H.: Nat. Lond. 404, 247 (2000)ADSCrossRefGoogle Scholar
  2. 2.
    Sackett C.A. et al.: Nat. Lond. 404, 256 (2000)ADSCrossRefGoogle Scholar
  3. 3.
    Julsgaard B. et al.: Nat. Lond. 413, 400 (2001)ADSCrossRefGoogle Scholar
  4. 4.
    Berkley A.J. et al.: Science 3000, 1548 (2003)ADSCrossRefGoogle Scholar
  5. 5.
    Bennett C.H. et al.: Phys. Rev. Lett. 70, 1895 (1993)MathSciNetADSMATHCrossRefGoogle Scholar
  6. 6.
    Bennett C.H., Wiesner S.J.: Phys. Rev. Lett. 69, 2881 (1992)MathSciNetADSMATHCrossRefGoogle Scholar
  7. 7.
    Pati A.K.: Phys. Rev. A 63, 014320 (2000)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Dur W., Vidal G., Cirac J.I., Linden N., Popescu S.: Phys. Rev. Lett. 87, 137901 (2001)ADSCrossRefGoogle Scholar
  9. 9.
    Anandan J., Aharonov Y.: Phys. Rev. Lett. 65, 1697 (1990)MathSciNetADSMATHCrossRefGoogle Scholar
  10. 10.
    Pati A.K.: Phys. Lett. A 159, 105 (1991)MathSciNetADSCrossRefGoogle Scholar
  11. 11.
    Pati A.K.: Phys. Rev. A 52, 2576 (1995)MathSciNetADSCrossRefGoogle Scholar
  12. 12.
    Brody D.C.: J. Phys. A Math. Gen. 36, 5587 (2003)MathSciNetADSMATHCrossRefGoogle Scholar
  13. 13.
    Brody D.C., Hook D.W.: J. Phys. A: Math. Gen. 39, L167 (2006)MathSciNetADSMATHCrossRefGoogle Scholar
  14. 14.
    Carlini A., Hosoya A., Koike T., Okudaira Y.: Phys. Rev. Lett. 96, 060503 (2006)ADSCrossRefGoogle Scholar
  15. 15.
    Giovannetti V., Lloyd S., Maccone L.: Europhys. Lett. 62, 615 (2002)ADSCrossRefGoogle Scholar
  16. 16.
    Margolus N., Levitin L.B.: Physica D 120, 188 (1998)ADSCrossRefGoogle Scholar
  17. 17.
    Giovannetti V., Lloyd S., Maccone L.: Phys. Rev. A 67, 052109 (2003)ADSCrossRefGoogle Scholar
  18. 18.
    Borras A., Zander C., Plastino A.R., Casas M., Plastino A.: Eruophys. Lett. 81, 30007 (2008)MathSciNetADSCrossRefGoogle Scholar
  19. 19.
    Pati A.K.: Phys. Lett. A 262, 296 (1999)MathSciNetADSMATHCrossRefGoogle Scholar
  20. 20.
    Childs A.M., Leung D.W., Verstraete F., Vidal G.: Quantum Inf. Comput. 3, 97 (2003)MathSciNetMATHGoogle Scholar
  21. 21.
    Wang X., Sanders B.C.: Phys. Rev. A 68, 014301 (2003)ADSCrossRefGoogle Scholar
  22. 22.
    Bennett C.H., Harrow A.W., Leung D.W., Smolin J.A.: IEEE Trans. Inf. Theory 49, 1895 (2003)MathSciNetCrossRefGoogle Scholar
  23. 23.
    Childs A.M., Leung D.W., Vidal G.: IEEE Trans. Inf. Theory 50, 1189 (2004)MathSciNetCrossRefGoogle Scholar
  24. 24.
    Bandyopadhyay S., Lidar D.A.: Phys. Rev. A 70, 0101301 (2004)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Lari B., Hassan A.S.M., Joag P.: Phys. Rev. A 80, 062305 (2009)ADSCrossRefGoogle Scholar
  26. 26.
    Pati A.K., Sahu P.K.: Phys. Lett. A 367, 177 (2007)MathSciNetADSMATHCrossRefGoogle Scholar
  27. 27.
    Nielsen M.A., Bremner M.J., Dodd J.L., Childs A.M., Dawson C.M.: Phys. Rev. A 66, 022317 (2002)MathSciNetADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Arun Kumar Pati
    • 1
  • Biswajit Pradhan
    • 2
  • Pankaj Agrawal
    • 3
  1. 1.Quantum Information and Computation GroupHarish Chandra Research Institute (HRI)Jhunsi, AllahabadIndia
  2. 2.International Institute of Information Technology, GothapatnaMalipada, BhubaneswarIndia
  3. 3.Institute of PhysicsBhubaneswarIndia

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