Skip to main content
SpringerLink
Log in

Probabilistic cloning of three nonorthogonal states

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

We study the probabilistic cloning of three nonorthogonal states with equal success probabilities. For simplicity, we assume that the three states belong to a special set. Analytical form of the maximal success probability for \(M\rightarrow N\) probabilistic cloning is calculated. With the maximal success probability, we deduce the explicit form of \(M\rightarrow N\) probabilistic quantum cloning machine. In the case of \(1\rightarrow 2\) cloning, we get the unambiguous form of the unitary operation. It is demonstrated that the upper bound for probabilistic quantum cloning machine in (Qiu in J Phys A 35:6931, 2002) can be reached only if the three states are equidistant.

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.

Institutional subscriptions

Fig. 1

Similar content being viewed by others

References

  1. Wootters, W.K., Zurek, W.H.: A single quantum cannot be cloned. Nat. (Lond.) 299, 802 (1982)

    Article  ADS  Google Scholar 

  2. Bǔzek, V., Hillery, M.: Quantum copying: beyond the no-cloning theorem. Phys. Rev. A 54, 1844 (1996)

    Article  ADS  MathSciNet  Google Scholar 

  3. van Enk, S.J.: Relations between cloning and the universal NOT derived from conservation laws. Phys. Rev. Lett. 95, 010502 (2005)

    Article  Google Scholar 

  4. Ricci, M., et al.: Separating the classical and quantum information via quantum cloning. Phys. Rev. Lett. 95, 090504 (2005)

    Article  ADS  Google Scholar 

  5. Fan, H., Imai, H., Matsumoto, K., Wang, X.B.: Phase-covariant quantum cloning of qudits. Phys. Rev. A 67, 022317 (2003)

    Article  ADS  Google Scholar 

  6. Navez, P., Cerf, N.J.: Cloning a real d-dimensional quantum state on the edge of the no-signaling condition. Phys. Rev. A 68, 032313 (2003)

    Article  ADS  Google Scholar 

  7. Zhang, W.H., Wu, T., Ye, L., Dai, J.L.: Optimal real state cloning in d dimensions. Phys. Rev. A 75, 044303 (2007)

    Article  ADS  Google Scholar 

  8. Niu, C.S., Griffiths, R.B.: Two-qubit copying machine for economical quantum eavesdropping. Phys. Rev. A 60, 2764 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  9. Fiurášek, J.: Optical implementations of the optimal phase-covariant quantum cloning machine. Phys. Rev. A 67, 052314 (2003)

    Article  ADS  Google Scholar 

  10. Buscemi, F., DAriano, G.M., Macchiavello, C.: Economical phase-covariant cloning of qudits. Phys. Rev. A 71, 042327 (2005)

    Article  ADS  Google Scholar 

  11. Durt, T., Fiurasek, J., Cerf, N.J.: Economical quantum cloning in any dimension. Phys. Rev. A 72, 052322 (2005)

  12. Zhang, W.H., Ye, L.: Optimal asymmetric phase-covariant and real state cloning in d dimensions. New J. Phys. 9, 318 (2007)

    Article  MathSciNet  Google Scholar 

  13. Scarani, V., Iblisdir, S., Gisin, N., Acín, A.: Quantum cloning. Rev. Mod. Phys. 77, 1225 (2005)

    Article  ADS  MATH  Google Scholar 

  14. Černoch, A., et al.: Experimental phase-covariant cloning of polarization states of single photons. Phys. Rev. A 74, 042327 (2006)

    Article  ADS  Google Scholar 

  15. Soubusta, J., Bartuskova, L., Cernoch, A., Fiurasek, J., Dusek, M.: Several experimental realizations of symmetric phase-covariant quantum cloners of single-photon qubits. Phys. Rev. A 76, 042318 (2007)

    Article  ADS  Google Scholar 

  16. Nagali, E., DeAngelis, T., Sciarrino, F., DeMartini, F.: Experimental realization of macroscopic coherence by phase-covariant cloning of a single photon. Phys. Rev. A 76, 042126 (2007)

    Article  ADS  Google Scholar 

  17. Sabuncu, M., Andersen, U.L., Leuchs, G.: Experimental demonstration of continuous variable cloning with phase-conjugate inputs. Phys. Rev. Lett. 98, 170503 (2007)

    Article  ADS  Google Scholar 

  18. Du, J.F., et al.: Experimental quantum cloning with prior partial information. Phys. Rev. Lett. 94, 040505 (2005)

    Article  ADS  Google Scholar 

  19. Cummins, H.K., et al.: Approximate quantum cloning with nuclear magnetic resonance. Phys. Rev. Lett. 88, 187901 (2002)

    Article  ADS  Google Scholar 

  20. Chen, H.W., Zhou, X., Suter, D., Du Phys, J.F.: Experimental realization of 1\(\rightarrow \)2 asymmetric phase-covariant quantum cloning. Phys. Rev. A 75, 012317 (2007)

    Article  ADS  Google Scholar 

  21. Duan, L.M., Guo, G.C.: Probabilistic cloning and identification of linearly independent quantum states. Phys. Rev. Lett. 80, 4999 (1998)

    Article  ADS  Google Scholar 

  22. Galvão, E.F., Hardy, L.: Cloning and quantum computation. Phys. Rev. A 62, 022301 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  23. Pati, A.K.: Quantum superposition of multiple clones and the novel cloning machine. Phys. Rev. Lett. 83, 2849 (1999)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  24. Qiu, D.W.: Novel cloning machine with supplementary information. J. Phys. A 39, 5135 (2006)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  25. Azuma, K., Shimamura, J., Koashi, M., Imoto, N.: Probabilistic cloning with supplementary information. Phys. Rev. A 72, 032335 (2005)

    Article  ADS  Google Scholar 

  26. Li, L., Qiu, D.W.: Probabilistic cloning with supplementary information contained in the quantum states of two auxiliary systems. Phys. Lett. A 362, 143 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  27. Chefles, A., Barnett, S.M.: Strategies and networks for state-dependent quantum cloning. Phys. Rev. A 60, 136 (1999)

    Article  ADS  Google Scholar 

  28. Zhang, C.W., Wang, Z.Y., Li, C.F., Guo, G.C.: Realizing probabilistic identification and cloning of quantum states via universal quantum logic gates. Phys. Rev. A 61, 062310 (2000). C F

    Article  ADS  MathSciNet  Google Scholar 

  29. Chefles, A., Barnett, S.M.: Quantum state separation, unambiguous discrimination and exact cloning. J. Phys. A 31, 10097 (1998)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  30. Qiu, D.W.: Upper bound on the success probability of separation among quantum states. J. Phys. A 35, 6931 (2002)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  31. Duan, L.M., Guo, G.C.: A probabilistic cloning machine for replicating two non-orthogonal states. Phys. Lett. A 243, 261 (1998)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  32. Guruprasad, K., Ramij, R.: Local cloning of multipartite entangled states. Quantum Inf. Process. 11, 711 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  33. Zhang, W.H., Dai, J.L., Cao, Z.L., Yang, M.: Probabilistic quantum cloning of real states. Opt. Commun. 283, 1956 (2010)

    Article  ADS  Google Scholar 

  34. Zhang, W.H., Yu, L.B., Cao, Z.L., Ye, L.: Optimal cloning of two known nonorthogonal quantum states. Phys. Rev. A 86, 022322 (2012)

    Article  ADS  Google Scholar 

  35. Araneda, G., Cisternas, N., Jiménez, O., Delgado, A.: Nonlocal optimal probabilistic cloning of qubit states via twin photons. Phys. Rev. A 86, 052332 (2012)

    Article  ADS  Google Scholar 

  36. Zhang, W., Rui, P.S., Zhang, Z.Y., Yang, Q.: Probabilistically cloning two single-photon states by using weak cross-Kerr nonlinearities. New J. Phys. 16, 083019 (2014)

    Article  ADS  Google Scholar 

  37. Chen, H.W., et al.: Experimental demonstration of probabilistic quantum cloning. Phys. Rev. Lett. 106, 180404 (2011)

    Article  ADS  Google Scholar 

  38. Jiménez, O., Bergou, J., Delgado, A.: Probabilistic cloning of three symmetric states. Phys. Rev. A 82, 062307 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  39. Jiménez, O., Roa, L., Delgado, A.: Probabilistic cloning of equidistant states. Phys. Rev. A 82, 022328 (2010)

    Article  ADS  Google Scholar 

Download references

Acknowledgments

This work is supported by the 211 Project of Anhui University, the National Science Foundation of China (11374013), and the Anhui Provincial Natural Science Foundation (1408085QF127).

Author information

Authors and Affiliations

  1. Key Laboratory of Optoelectronic Information Acquisition and Manipulation of Ministry of Education of China, School of Physics and Material Science, Anhui University, Hefei, 230601, China

    Wen Zhang, Qun Yang & Ziyun Zhang

  2. Anhui Xinhua University, Hefei, 230088, China

    Pinshu Rui

  3. Department of Physics, Anhui Medical University, Hefei, 230032, China

    Yan Zhao

Authors
  1. Wen Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Pinshu Rui
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Qun Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yan Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Ziyun Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wen Zhang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, W., Rui, P., Yang, Q. et al. Probabilistic cloning of three nonorthogonal states. Quantum Inf Process 14, 1523–1534 (2015). https://doi.org/10.1007/s11128-015-0921-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11128-015-0921-4

Keywords

Search

Navigation