Advertisement

Coherence and entanglement under three-qubit cloning operations

  • Suchetana GoswamiEmail author
  • Satyabrata Adhikari
  • A. S. Majumdar
Article

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.

Keywords

Quantum correlations Coherence Entanglement Cloning operations 

References

  1. 1.
    Einstein, A., Podolsky, D., Rosen, N.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777 (1935)ADSzbMATHGoogle Scholar
  2. 2.
    Schrödinger, E.: Discussion of probability relations between separated systems. Proc. Camb. Philos. Soc. 31, 555 (1935)ADSCrossRefGoogle Scholar
  3. 3.
    Schrödinger, E.: Discussion of probability relations between separated systems. Proc. Camb. Philos. Soc. 32, 446 (1936)ADSCrossRefGoogle Scholar
  4. 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)ADSMathSciNetCrossRefGoogle Scholar
  5. 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)ADSMathSciNetCrossRefGoogle Scholar
  6. 6.
    Bell, J.S.: On the Einstein Podolsky Rosen paradox. Physics 1, 195 (1964)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Nielsen, M., Chuang, I.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)zbMATHGoogle Scholar
  8. 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)ADSMathSciNetCrossRefGoogle Scholar
  9. 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)ADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    Ekert, A.K.: Quantum cryptography based on Bells theorem. Phys. Rev. Lett. 67, 661 (1991)ADSMathSciNetCrossRefGoogle Scholar
  11. 11.
    Horodecki, R., Horodecki, P., Horodecki, M., Horodecki, K.: Quantum entanglement. Rev. Mod. Phys. 81, 865 (2009)ADSMathSciNetCrossRefGoogle Scholar
  12. 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)ADSMathSciNetCrossRefGoogle Scholar
  13. 13.
    Michler, M., Weinfurter, H., Zukowski, M.: Experiments towards Falsification of noncontextual hidden variable theories. Phys. Rev. Lett. 84, 5457 (2000)ADSCrossRefGoogle Scholar
  14. 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)CrossRefGoogle Scholar
  15. 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)CrossRefGoogle Scholar
  16. 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)ADSCrossRefGoogle Scholar
  17. 17.
    Baumgratz, T., Cramer, M., Plenio, M.B.: Quantifying coherence. Phys. Rev. Lett. 113, 140401 (2014)ADSCrossRefGoogle Scholar
  18. 18.
    Girolami, D.: Observable measure of quantum coherence in finite dimensional systems. Phys. Rev. Lett. 113, 170401 (2014)ADSCrossRefGoogle Scholar
  19. 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)ADSCrossRefGoogle Scholar
  20. 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)ADSCrossRefGoogle Scholar
  21. 21.
    berg, J.: Catalytic coherence. Phys. Rev. Lett. 113, 150402 (2014)CrossRefGoogle Scholar
  22. 22.
    Narasimhachar, V., Gour, G.: Low-temperature thermodynamics with quantum coherence. Nat. Commun. 6, 7689 (2015)ADSCrossRefGoogle Scholar
  23. 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)CrossRefGoogle Scholar
  24. 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)ADSCrossRefGoogle Scholar
  25. 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)ADSCrossRefGoogle Scholar
  26. 26.
    Marvian, I., Spekkens, R.W., Zanardi, P.: Quantum speed limits, coherence, and asymmetry. Phys. Rev. A 93, 052331 (2016)ADSCrossRefGoogle Scholar
  27. 27.
    Streltsov, A., Singh, U., Dhar, H.S., Bera, M.N., Adesso, G.: Measuring quantum coherence with entanglement. Phys. Rev. Lett. 115, 020403 (2015)ADSMathSciNetCrossRefGoogle Scholar
  28. 28.
    Mondal, D., Pramanik, T., Pati, A.K.: Nonlocal advantage of quantum coherence. Phys. Rev. A 95, 010301 (2017)ADSMathSciNetCrossRefGoogle Scholar
  29. 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)ADSCrossRefGoogle Scholar
  30. 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)ADSCrossRefGoogle Scholar
  31. 31.
    Luo, Y., Li, Y., Hsieh, M-H: Inequivalent multipartite coherence classes and new coherence monotones. arxiv:1807.06308
  32. 32.
    Wootters, W.K., Zurek, W.H.: A single quantum cannot be cloned. Nat. (Lond.) 299, 802 (1982)ADSCrossRefGoogle Scholar
  33. 33.
    Buzek, V., Hillery, M.: Quantum copying: beyond the no-cloning theorem. Phys. Rev. A 54, 1844 (1996)ADSMathSciNetCrossRefGoogle Scholar
  34. 34.
    Bruss, D., Cinchetti, M., DAriano, G.M., Macchiavello, C.: Phase-covariant quantum cloning. Phys. Rev. A 62, 12302 (2000)ADSCrossRefGoogle Scholar
  35. 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)ADSCrossRefGoogle Scholar
  36. 36.
    Streltsov, A., Adesso, G., Plenio, M.B.: Colloquium: quantum coherence as a resource. Rev. Mod. Phys. 89, 041003 (2017)ADSMathSciNetCrossRefGoogle Scholar
  37. 37.
    Coffman, V., Kundu, J., Wootters, W.K.: Distributed entanglement. Phys. Rev. A 61, 052306 (2000)ADSCrossRefGoogle Scholar
  38. 38.
    Ying, M.: WoottersZurek Quantum-copying machine: the higher-dimensional case. Phys. Lett. A 299, 107 (2002)ADSMathSciNetCrossRefGoogle Scholar
  39. 39.
    Wootters, W.K.: Entanglement of formation of an arbitrary state of two qubits. Phys. Rev. Lett. 80, 2245 (1998)ADSCrossRefGoogle Scholar
  40. 40.
    O’Connor, K.M., Wootters, W.K.: Entangled rings. Phys. Rev. A 63, 052302 (2000)ADSCrossRefGoogle Scholar
  41. 41.
    Bruss, D., Macchiavello, C.: On the entanglement structure in quantum cloning. Found. Phys. 33, 1617 (2003)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Suchetana Goswami
    • 1
    Email author
  • Satyabrata Adhikari
    • 2
  • A. S. Majumdar
    • 1
  1. 1.S. N. Bose National Centre for Basic SciencesSalt LakeIndia
  2. 2.Delhi Technological UniversityNew DelhiIndia

Personalised recommendations