Quantum Information Processing

, Volume 12, Issue 4, pp 1701–1717 | Cite as

Distort one qubit from copying and deleting

  • Ming-Xing Luo
  • Yun Deng


Immeasurability of a quantum state has important consequence in practical implementation of quantum computers. Our purpose is to analyze the efficiency of the entangled output of Pati-Braunstein deleting machine or Wootters-Zurek quantum copying machine as a quantum channel. Interestingly we find that for special values of the input parameter the state does not violate the Bell’s inequality. Moreover, we analyze the performances of the entangled output of Pati-Braunstein deleting after the Wootters-Zurek copying machine.


Pati-Braunstein deleting Wootters-Zurek copying Bell’s inequality Distortion 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Wootters W.K., Zurek W.H.: A single quantum cannot be cloned. Nature 299, 802 (1982)ADSCrossRefGoogle Scholar
  2. 2.
    Yuen H.P.: Amplification of quantum states and noiseless photon amplifiers. Phys. Lett. A 113, 405 (1986)MathSciNetADSCrossRefGoogle Scholar
  3. 3.
    Duan L.M., Guo G.C.: A probabilistic cloning machine for replicating two non-orthogonal states. Phys. Lett. A 243, 261 (1998)MathSciNetADSzbMATHCrossRefGoogle Scholar
  4. 4.
    Duan L.M., Guo G.C.: Probabilistic cloning and identification of linearly independent quantum states. Phys. Rev. Lett. 80, 4999 (1998)ADSCrossRefGoogle Scholar
  5. 5.
    Pati A.K.: Quantum superposition of multiple clones and the novel cloning machine. Phys. Rev. Lett. 83, 2849 (1999)MathSciNetADSzbMATHCrossRefGoogle Scholar
  6. 6.
    Cerf N.: Asymmetric quantum cloning machines in any dimension. J. Mod. Opt. 47, 187 (2000)MathSciNetADSGoogle Scholar
  7. 7.
    Gisin N., Massar S.: Optimal quantum cloning machines. Phys. Rev. Lett. 79, 2153 (1997)ADSCrossRefGoogle Scholar
  8. 8.
    Bruß D., Ekert A., Macchavello C.: Optimal universal quantum cloning and state estimation. Phys. Rev. Lett. 81, 2598 (1998)ADSCrossRefGoogle Scholar
  9. 9.
    Bužek V., Hillery M.H.: Universal optimal cloning of arbitrary quantum states: from qubits to quantum registers. Phys. Rev. Lett. 81, 5003 (1998)ADSCrossRefGoogle Scholar
  10. 10.
    Fan H., Imai H., Matsumoto K., Wang X.-B.: Phase-covariant quantum cloning of qudits. Phys. Rev. A 67, 022317 (2003)ADSCrossRefGoogle Scholar
  11. 11.
    Sacchi M.F.: Phase-covariant cloning of coherent states. Phys. Rev. A 75, 042328 (2007)ADSCrossRefGoogle Scholar
  12. 12.
    Kay A., Kaszlikowski D., Ramanathan R.: Optimal cloning and singlet monogamy. Phys. Rev. Lett. 103, 050501 (2009)ADSCrossRefGoogle Scholar
  13. 13.
    Bartkiewicz K., Miranowicz A., Özdemir S.K.: Optimal mirror phase-covariant cloning. Phys. Rev. A 80, 032306 (2009)ADSCrossRefGoogle Scholar
  14. 14.
    Massar S., Popescu S.: Optimal extraction of information from finite quantum ensembles. Phys. Rev. Lett. 74, 1259 (1995)MathSciNetADSzbMATHCrossRefGoogle Scholar
  15. 15.
    Derka R., Bužek V., Ekert A.: Universal algorithm for optimal estimation of quantum states from finite ensembles via realizable generalized measurement. Phys. Rev. Lett. 80, 1571 (1998)MathSciNetADSzbMATHCrossRefGoogle Scholar
  16. 16.
    Dobšíček M., Johansson G., Shumeiko V., Wendin G.: Arbitrary accuracy iterative quantum phase estimation algorithm using a single ancillary qubit: a two-qubit benchmark. Phys. Rev. A 76, 030306(R) (2007)ADSGoogle Scholar
  17. 17.
    García-Mata I., Shepelyansky D.L.: Quantum phase estimation algorithm in presence of static imperfections. Eur. Phys. J. D 47, 151–156 (2008)ADSCrossRefGoogle Scholar
  18. 18.
    Bennett C.H., Brassard G., Crépeau 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)MathSciNetADSzbMATHCrossRefGoogle Scholar
  19. 19.
    Szilard L.: Uber die Entropieverminderung in einem thermodynamischen System bei Eingriffen intelligenter Wesen. Z.Phys 53, 840 (1929)ADSzbMATHCrossRefGoogle Scholar
  20. 20.
    Landauer R.: Irreversibility and heat generation in the computing proce. IBM J. Res. Dev. 3, 183 (1961)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Zurek W.H.: Quantum cloning: Schrödinger’s sheep. Nature 404, 131 (2000)CrossRefGoogle Scholar
  22. 22.
    Pati A.K., Braunstein S.L.: Impossibility of deleting an unknown quantum state. Nature 404, 164 (2000)ADSCrossRefGoogle Scholar
  23. 23.
    Pati A.K., Braunstein S.L.: Quantum no-deleting principle and some of its implications. arXiv:quant-ph/0007121v1Google Scholar
  24. 24.
    Bužek V., Hillery M.H.: Quantum copying: beyond the no-cloning theorem. Phys. Rev. A 54, 1844–1852 (1996)MathSciNetADSCrossRefGoogle Scholar
  25. 25.
    Peres A.: Separability criterion for density matrices. Phys. Rev. Lett. 77, 1413 (1996)MathSciNetADSzbMATHCrossRefGoogle Scholar
  26. 26.
    Horodecki M., Horodecki P., Horodecki R.: Separability of mixed states: necessary and sufficient conditions. Phys. Lett. A 223, 1 (1996)MathSciNetADSzbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Information Security Center, School of Information Science and TechnologySouthwest Jiaotong UniversityChengduChina
  2. 2.Institute of Computer ScienceSichuan University of Science EngineeringZigongChina

Personalised recommendations