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International Journal of Theoretical Physics

, Volume 57, Issue 12, pp 3776–3784 | Cite as

Amending Coherence-Breaking Channels via Unitary Operations

  • Long-Mei Yang
  • Bin Chen
  • Tao Li
  • Shao-Ming Fei
  • Zhi-Xi WangEmail author
Article

Abstract

The coherence-breaking channels play a significant role in quantum information theory. We study the coherence-breaking channels and give a method to amend the coherence-breaking channels by applying unitary operations. For given incoherent channel Φ, we give necessary and sufficient conditions for the channel to be a coherence-breaking channel and amend it via unitary operations. For qubit incoherent channels Φ that are not coherence-breaking ones, we consider the mapping Φ ∘Φ and present the conditions for coherence-breaking and channel amendment as well.

Keywords

Coherence-breaking channel Incoherent channel Coherence-breaking index 

Notes

Acknowledgements

This work is supported by the NSFC (11675113) and the Research Foundation for Youth Scholars of Beijing Technology and Business University (QNJJ2017-03) and the Scientific Research General Program of Beijing Municipal Commission of Education (Grant No. KM201810011009).

References

  1. 1.
    Bartlett, S.D., Rudolph, T., Spekkens, R.W.: Reference frames, superselection rules, and quantum information. Rev. Mod. Phys. 79, 555 (2007)ADSMathSciNetCrossRefGoogle Scholar
  2. 2.
    Marvian, I., Spekkens, R.W.: The theory of manipulations of pure state asymmetry: I. Basic tools, equivalence classes and single copy transformations. J. Phys. 15, 033001 (2013)Google Scholar
  3. 3.
    Marvian, I., Spekkens, R.W.: Modes of asymmetry: The application of harmonic analysis to symmetric quantum dynamics and quantum reference frames. Phys. Rev. A 90, 062110 (2014)ADSCrossRefGoogle Scholar
  4. 4.
    Lloyd, S.: Quantum coherence in biological systems. J. Phys. Conf. Ser. 302, 012037 (2011)CrossRefGoogle Scholar
  5. 5.
    Lambert, N., Chen, Y.N., Chen, Y.C., Li, C.M., Chen, G.Y., Nori, F.: Quantum biology. Nat. Phys. 9, 10 (2013)CrossRefGoogle Scholar
  6. 6.
    Åberg, J: Catalytic coherence. Phys. Rev. Lett. 113, 150402 (2013) (2014)CrossRefGoogle Scholar
  7. 7.
    Ćwikliński, P., Studziński, 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)ADSCrossRefGoogle Scholar
  8. 8.
    Baumgratz, T., Cramer, M., Plenio, M.B.: Quantifying coherence. Phys. Rev. Lett. 113, 140401 (2014)ADSCrossRefGoogle Scholar
  9. 9.
    Yadin, B., Ma, J., Girolami, D., Gu, M., Vedral, V.: Quantum processes which do not use coherence. Phys. Rev. X 6, 041028 (2016)Google Scholar
  10. 10.
    Chitambar, E., Gour, G.: Critical examination of incoherent operations and a physically consistent resource theory of quantum coherence. Phys. Rev. Lett. 117, 030401 (2016)ADSCrossRefGoogle Scholar
  11. 11.
    Chen, B., Li, Y.: Coherent state transfer through a multi-channel quantum network: Natural versus controlled evolution passage. Sci. China-Phys. Mech. Astron. 59, 640302 (2018)CrossRefGoogle Scholar
  12. 12.
    Deng, F.G., Ren, B.C., Li, X.H.: Quantum hyperentanglement and its applications in quantum information processing. Sci. Bull. 62, 46–68 (2017)CrossRefGoogle Scholar
  13. 13.
    Wei, S.J., Xin, T., Long, G.L.: Efficient universal quantum channel simulation in IBM’s cloud quantum computer. Sci. China-Phys. Mech. Astron. 61, 070311 (2018)ADSCrossRefGoogle Scholar
  14. 14.
    Wei, T., Pedernales, S.J., Solano, E., Long, G.L.: Quantum simulation of quantum channels in nuclear magnetic resonance. Phys. Rev. A 96, 062303 (2017)ADSCrossRefGoogle Scholar
  15. 15.
    Zhao, M.J., Ma, T., Ma, Y.Q.: Coherent evolution in two-qubit system going through amplitude damping channel. Sci. China-Phys. Mech. Astron. 61, 020311 (2018)ADSCrossRefGoogle Scholar
  16. 16.
    Hou, S.Y., Long, G.L.: Experimental quantum Hamiltonian identification from measurement time traces. Sci. Bull. 62, 863–868 (2017)CrossRefGoogle Scholar
  17. 17.
    Horodecki, M., Shor, P.W., Ruskai, M.B.: Entanglement-breaking channels. Rev. Math. Phys. 15, 629 (2003)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Ruskai, M.B.: Qubit entanglement-breaking channels. Rev. Math. Phys. 15, 643 (2003)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Knoll, L.T., Schmiegelow, C.T., Farías, O. J., Walborn, S.P., Larotonda, M.A.: Entanglement-breaking channels and entanglement sudden death. Phys. Rev. A 94, 012345 (2016)ADSCrossRefGoogle Scholar
  20. 20.
    Cuevas, A., Pasquale, A.D., Mari, A., Orieux, A., Duranti, S., Massaro, M., Carli, A.D., Roccia, E.: Amending entanglement-breaking channels via intermediate unitary operations. Phys. Rev. A 96, 022322 (2017)ADSCrossRefGoogle Scholar
  21. 21.
    Bu, K.F., Swati, Singh, U., Wu, J.: Coherence-breaking channels and coherence sudden death. Phys. Rev. A 94, 052335 (2016)ADSMathSciNetCrossRefGoogle Scholar
  22. 22.
    Nielson, M.A, Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press (2010)Google Scholar
  23. 23.
    Hu, X.Y.: Channels that do not generate coherence. Phys. Rev. A 94, 012326 (2016)ADSCrossRefGoogle Scholar
  24. 24.
    Bertlmann, R.A., Krammer, P.: Bloch vectors for qudits. J. Phys. A 41, 235303 (2008)ADSMathSciNetCrossRefGoogle Scholar
  25. 25.
    Marshman, R.J., Lund, A.P., Rohde, P.P., Ralph, T.C.: Passive quantum error correction of linear optics networks through error averaging. Phys. Rev. A 97, 022324 (2018)ADSCrossRefGoogle Scholar
  26. 26.
    Long, G.L.: General quantum interference principle and duality computer. Commun. Theor. Phys. 45, 825 (2006)ADSMathSciNetCrossRefGoogle Scholar
  27. 27.
    Long, G.L.: Duality quantum computing and duality quantum information process. Int. J. Theor. Phys. 50, 1305–1318 (2011)CrossRefGoogle Scholar
  28. 28.
    Ruskai, M.B., Szarek, S., Werner, E.: An analysis of completely-positive trace-preserving maps on M 2. Linear Algebra Appl. 347, 159 (2002)MathSciNetCrossRefGoogle Scholar
  29. 29.
    King, C., Ruskai, M.B.: Minimal entropy of states emerging from noisy quantum channels. IEEE Trans. Inf. Theory 47, 192 (2001)MathSciNetCrossRefGoogle Scholar

Copyright information

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

Authors and Affiliations

  • Long-Mei Yang
    • 1
  • Bin Chen
    • 2
  • Tao Li
    • 3
  • Shao-Ming Fei
    • 1
  • Zhi-Xi Wang
    • 1
    Email author
  1. 1.School of Mathematical SciencesCapital Normal UniversityBeijingChina
  2. 2.School of Mathematical SciencesTianjin Normal UniversityTianjinChina
  3. 3.School of Science, Beijing Technology and Business UniversityBeijingChina

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