[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ Skip to main content
Springer Nature Link
Log in

Coherence and entanglement under three-qubit cloning operations

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

Coherence and entanglement are the two most crucial resources for various quantum information processing tasks. Here, we study the interplay of coherence and entanglement under the action of different three-qubit quantum cloning operations. Considering certain well-known quantum cloning machines (input state independent and dependent), we provide examples of coherent and incoherent operations performed by them. We show that both the output entanglement and coherence could vanish under incoherent cloning operations. Coherent cloning operations, on the other hand, could be used to construct a universal and optimal coherence machine. It is also shown that under coherent cloning operations, the output two-qubit entanglement could be maximal even if the input coherence is negligible. Also it is possible to generate a fixed amount of entanglement independent of the nature of the input state.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (United Kingdom)

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Einstein, A., Podolsky, D., Rosen, N.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777 (1935)

    Article  ADS  Google Scholar 

  2. Schrödinger, E.: Discussion of probability relations between separated systems. Proc. Camb. Philos. Soc. 31, 555 (1935)

    Article  ADS  Google Scholar 

  3. Schrödinger, E.: Discussion of probability relations between separated systems. Proc. Camb. Philos. Soc. 32, 446 (1936)

    Article  ADS  Google Scholar 

  4. Wiseman, H.M., Jones, S.J., Doherty, A.C.: Steering, entanglement, nonlocality, and the Einstein–Podolsky–Rosen paradox. Phys. Rev. Lett. 98, 140402 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  5. Jones, S.J., Wiseman, H.M., Doherty, A.C.: Entanglement, Einstein–Podolsky–Rosen correlations, bell nonlocality, and steering. Phys. Rev. A 76, 052116 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  6. Bell, J.S.: On the Einstein Podolsky Rosen paradox. Physics 1, 195 (1964)

    Article  MathSciNet  Google Scholar 

  7. Nielsen, M., Chuang, I.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)

    MATH  Google Scholar 

  8. 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  Google Scholar 

  9. Bennett, C.H., Brassard, G., Crpeau, 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  Google Scholar 

  10. Ekert, A.K.: Quantum cryptography based on Bells theorem. Phys. Rev. Lett. 67, 661 (1991)

    Article  ADS  MathSciNet  Google Scholar 

  11. Horodecki, R., Horodecki, P., Horodecki, M., Horodecki, K.: Quantum entanglement. Rev. Mod. Phys. 81, 865 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  12. Boschi, D., Branca, S., De Martini, F., Hardy, L., Popescu, S.: Experimental realization of teleporting an unknown pure quantum state via dual classical and Einstein–Podolsky–Rosen channels. Phys. Rev. Lett. 80, 1121 (1998)

    Article  ADS  MathSciNet  Google Scholar 

  13. Michler, M., Weinfurter, H., Zukowski, M.: Experiments towards Falsification of noncontextual hidden variable theories. Phys. Rev. Lett. 84, 5457 (2000)

    Article  ADS  Google Scholar 

  14. Barreiro, J.T., Wei, T.-C., Kwiat, P.G.: Beating the channel capacity limit for linear photonic superdense coding. Nat. Phys. 4, 282 (2008)

    Article  Google Scholar 

  15. Berta, M., Christandl, M., Colbeck, R., Renes, J.M., Renner, R.: The uncertainty principle in the presence of quantum memory. Nat. Phys. 6, 659 (2010)

    Article  Google Scholar 

  16. Pramanik, T., Chowdhury, P., Majumdar, A.S.: Fine-grained lower limit of entropic uncertainty in the presence of quantum memory. Phys. Rev. Lett. 110, 020402 (2013)

    Article  ADS  Google Scholar 

  17. Baumgratz, T., Cramer, M., Plenio, M.B.: Quantifying coherence. Phys. Rev. Lett. 113, 140401 (2014)

    Article  ADS  Google Scholar 

  18. Girolami, D.: Observable measure of quantum coherence in finite dimensional systems. Phys. Rev. Lett. 113, 170401 (2014)

    Article  ADS  Google Scholar 

  19. Napoli, C., Bromley, T.R., Cianciaruso, M., Piani, M., Johnston, N., Adesso, G.: Robustness of coherence: an operational and observable measure of quantum coherence. Phys. Rev. Lett. 116, 150502 (2016)

    Article  ADS  Google Scholar 

  20. Yao, Y., Dong, G.H., Xiao, X., Sun, C.P.: Frobenius-norm-based measures of quantum coherence and asymmetry. Sci. Rep. 6, 32010 (2016)

    Article  ADS  Google Scholar 

  21. berg, J.: Catalytic coherence. Phys. Rev. Lett. 113, 150402 (2014)

    Article  Google Scholar 

  22. Narasimhachar, V., Gour, G.: Low-temperature thermodynamics with quantum coherence. Nat. Commun. 6, 7689 (2015)

    Article  ADS  Google Scholar 

  23. wikliski, P., Studziski, M., Horodecki, M., Oppenheim, J.: Limitations on the evolution of quantum coherences: towards fully quantum second laws of thermodynamics. Phys. Rev. Lett. 115, 210403 (2015)

    Article  Google Scholar 

  24. Gour, G., Marvian, I., Spekkens, R.W.: Measuring the quality of a quantum reference frame: the relative entropy of frameness. Phys. Rev. A 80, 012307 (2009)

    Article  ADS  Google Scholar 

  25. Marvian, I., Spekkens, R.W.: The theory of manipulations of pure state asymmetry: I. Basic tools, equivalence classes and single copy transformations. New J. Phys. 15, 033001 (2013)

    Article  ADS  Google Scholar 

  26. Marvian, I., Spekkens, R.W., Zanardi, P.: Quantum speed limits, coherence, and asymmetry. Phys. Rev. A 93, 052331 (2016)

    Article  ADS  Google Scholar 

  27. Streltsov, A., Singh, U., Dhar, H.S., Bera, M.N., Adesso, G.: Measuring quantum coherence with entanglement. Phys. Rev. Lett. 115, 020403 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  28. Mondal, D., Pramanik, T., Pati, A.K.: Nonlocal advantage of quantum coherence. Phys. Rev. A 95, 010301 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  29. Jung, E., Hwang, M.-R., Ju, Y.H., Kim, M.-S., Yoo, S.-K., Kim, H., Park, D., Son, J.-W., Tamaryan, S., Cha, S.-K.: Greenberger–Horne–Zeilinger versus W states: quantum teleportation through noisy channels. Phys. Rev. A 78, 012312 (2008)

    Article  ADS  Google Scholar 

  30. Kang, Y.-H., Chen, Y.-H., Wu, Q.-C., Huang, B.-H., Song, J., Xia, Y.: Fast generation of W states of superconducting qubits with multiple Schrodinger dynamics. Sci. Rep. 6, 36737 (2016)

    Article  ADS  Google Scholar 

  31. Luo, Y., Li, Y., Hsieh, M-H: Inequivalent multipartite coherence classes and new coherence monotones. arxiv:1807.06308

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

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  34. Bruss, D., Cinchetti, M., DAriano, G.M., Macchiavello, C.: Phase-covariant quantum cloning. Phys. Rev. A 62, 12302 (2000)

    Article  ADS  Google Scholar 

  35. Bruss, D., DiVincenzo, D.P., Ekert, A., Fuchs, C.A., Macchiavello, C., Smolin, J.A.: Optimal universal and state-dependent quantum cloning. Phys. Rev. A 57, 2368 (1998)

    Article  ADS  Google Scholar 

  36. Streltsov, A., Adesso, G., Plenio, M.B.: Colloquium: quantum coherence as a resource. Rev. Mod. Phys. 89, 041003 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  37. Coffman, V., Kundu, J., Wootters, W.K.: Distributed entanglement. Phys. Rev. A 61, 052306 (2000)

    Article  ADS  Google Scholar 

  38. Ying, M.: WoottersZurek Quantum-copying machine: the higher-dimensional case. Phys. Lett. A 299, 107 (2002)

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

  40. O’Connor, K.M., Wootters, W.K.: Entangled rings. Phys. Rev. A 63, 052302 (2000)

    Article  ADS  Google Scholar 

  41. Bruss, D., Macchiavello, C.: On the entanglement structure in quantum cloning. Found. Phys. 33, 1617 (2003)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. S. N. Bose National Centre for Basic Sciences, Block JD, Sector-III, Salt Lake, Kolkata, 700106, India

    Suchetana Goswami & A. S. Majumdar

  2. Delhi Technological University, Shahbad Daulatpur, Main Bawana Road, New Delhi, Delhi, 110042, India

    Satyabrata Adhikari

Authors
  1. Suchetana Goswami
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Satyabrata Adhikari
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. S. Majumdar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Suchetana Goswami.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Goswami, S., Adhikari, S. & Majumdar, A.S. Coherence and entanglement under three-qubit cloning operations. Quantum Inf Process 18, 36 (2019). https://doi.org/10.1007/s11128-018-2150-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-018-2150-0

Keywords

Search

Navigation