International Journal of Theoretical Physics

, Volume 58, Issue 11, pp 3651–3657 | Cite as

Formal Verification for KMB09 Protocol

  • Guiping DaiEmail author


The unifying of qACP and classical ACP under the framework of quantum process configuration 〈p, ρ〉 makes verification for quantum protocols possible, not only the pure quantum protocol, but also protocol that mixes quantum information and classical information. In this paper, we verify the KMB09 protocol by use of quantum process algebra qACP.


Quantum computing Quantum processes Process algebra Verification 



  1. 1.
    Baeten, J.C.M.: A brief history of process algebra. Theor. Comput. Sci. Process. Algebra 335(2–3), 131–146 (2005)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Milner, R.: Communication and concurrency. Prentice Hall (1989)Google Scholar
  3. 3.
    Milner, R., Parrow, J., Walker, D.: A calculus of mobile processes, Parts I and II. Inf. Comput. 1992(100), 1–77 (1992)CrossRefGoogle Scholar
  4. 4.
    Hoare, C.A.R.: Communicating sequential processes.
  5. 5.
    Fokkink, W.: Introduction to Process Algebra, 2nd edn. Springer, Berlin (2007)zbMATHGoogle Scholar
  6. 6.
    Feng, Y., Duan, R.Y., Ji, Z.F., Ying, M.S.: Probabilistic bisimulations for quantum processes. Inf. Comput. 2007(205), 1608–1639 (2007)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Gay, S.J., Nagarajan, R.: Communicating quantum processes. In: Proceedings of the 32nd ACM Symposium on Principles of Programming Languages, Long Beach, pp 145–157. ACM Press, California (2005)Google Scholar
  8. 8.
    Gay, S.J., Nagarajan, R.: Typechecking communicating quantum processes. Math. Struct. Comput. Sci. 2006(16), 375–406 (2006)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Jorrand, P., Lalire, M.: Toward a quantum process algebra. In: Proceedings of the 1st ACM conference on computing frontiers, pp 111–119. ACM Press, Ischia (2005)Google Scholar
  10. 10.
    Jorrand, P., Lalire, M.: From quantum physics to programming languages: a process algebraic approach. Lect. Notes Comput. Sci 2005(3566), 1–16 (2005)Google Scholar
  11. 11.
    Lalire, M.: Relations among quantum processes: Bisimilarity and congruence. Math. Struct. Comput. Sci. 2006(16), 407–428 (2006)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Lalire, M., Jorrand, P.: A process algebraic approach to concurrent and distributed quantum computation: operational semantics. In: Proceedings of the 2nd International Workshop on Quantum Programming Languages, TUCS General Publications, pp. 109–126 (2004)Google Scholar
  13. 13.
    Ying, M., Feng, Y., Duan, R., Ji, Z.: An algebra of quantum processes. ACM Trans. Comput. Log. 10(3), 1–36 (2009)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Feng, Y., Duan, R., Ying, M.: Bisimulations for quantum processes. In: Proceedings of the 38th ACM Symposium on Principles of Programming Languages (POPL 11), pp 523–534, ACM Press (2011)Google Scholar
  15. 15.
    Deng, Y., Feng, Y.: Open bisimulation for quantum processes. Manuscript, arXiv:1201.0416 (2012)
  16. 16.
    Feng, Y., Deng, Y., Ying, M.: Symbolic bisimulation for quantum processes. Manuscript, arXiv:1202.3484 (2012)
  17. 17.
    Wang, Y.: An Axiomatization for Quantum Processes to Unifying Quantum and Classical Computing. Manuscript, arXiv:1311.2960 (2013)
  18. 18.
    Wang, Y.: Entanglement in Quantum Process Algebra. Manuscript, arXiv:1404.0665 (2014)
  19. 19.
    Khan, M.M., Murphy, M., Beige, A.: High error-rate quantum key distribution for long-distance communication. arXiv:0901.3909v4 (2009)

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.College of Automation, Faculty of Information TechnologyBeijing University of TechnologyBeijingChina

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