Entanglement in Quantum Process Algebra

  • Yong WangEmail author


We explicitly model entanglement in quantum processes by treating entanglement as a kind of parallelism. We introduce a shadow constant quantum operation and a so-called entanglement merge into quantum process algebra qACP. The transition rules of the shadow constant quantum operation and entanglement merge are designed. We also do a sound and complete axiomatization modulo the so-called quantum bisimilarity for the shadow constant quantum operation and entanglement merge. Then, this new type entanglement merge is extended into the full qACP. The new qACP has wide use in verification for quantum protocols, since most quantum protocols have mixtures with classical and quantum information, and also there are many quantum protocols adopting entanglement.


Quantum mechanics Entanglement Quantum processes Process algebra 



  1. 1.
    Baeten, J.C.M.: A brief history of process algebra. Theor. Comput. Sci. Process Algebra 335(2–3), 131–146 (2005)MathSciNetCrossRefzbMATHGoogle 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)CrossRefzbMATHGoogle Scholar
  4. 4.
    Hoare, C.A.R.: Communicating Sequential Processes. (1985)
  5. 5.
    Fokkink, W.: Introduction to Process Algebra, 2nd edn. Springer (2007)Google Scholar
  6. 6.
    Plotkin, G.D.: A structural approach to operational semantics. Aarhus University, Tech Report DAIMIFN-19 (1981)Google Scholar
  7. 7.
    Feng, Y., Duan, R.Y., Ji, Z.F., Ying, M.S.: Probabilistic bisimulations for quantum processes. Inf. Comput. 2007(205), 1608–1639 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Gay, S.J., Nagarajan, R.: Communicating quantum processes. In: Proceedings of the 32nd ACM Symposium on Principles of Programming Languages, pp. 145–157. ACM Press, Long Beach (2005)Google Scholar
  9. 9.
    Gay, S.J., Nagarajan, R.: Typechecking communicating quantum processes. Math. Struct. Comput. Sci. 2006(16), 375–406 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    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
  11. 11.
    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
  12. 12.
    Lalire, M.: Relations among quantum processes: Bisimilarity and congruence. Math. Struct. Comput. Sci. 2006(16), 407–428 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    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, pp. 109–126. TUCS General Publications (2004)Google Scholar
  14. 14.
    Ying, M., Feng, Y., Duan, R., Ji, Z.: An algebra of quantum processes. ACM Trans. Comput. Logic (TOCL) 10(3), 1–36 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    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
  16. 16.
    Ekert, A.K.: Quantum cryptography based on Bell’s theorem. Phys. Rev. Lett. 67(6), 661–663 (1991)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Deng, Y., Feng, Y.: Open bisimulation for quantum processes. Manuscript, arXiv:1201.0416 (2012)
  18. 18.
    Feng, Y., Deng, Y., Ying, M.: Symbolic bisimulation for quantum processes. Manuscript, arXiv:1202.3484 (2012)
  19. 19.
    Wang, Y.: An axiomatization for quantum processes to unifying quantum and classical computing. Manuscript, arXiv:1311.2960 (2013)
  20. 20.
    Duncan, R.: Types for Quantum Computing. Ph.D. Dessertation, Oxford University (2006)Google Scholar

Copyright information

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

Authors and Affiliations

  1. 1.College of Computer Science and Technology, Faculty of Information TechnologyBeijing University of TechnologyBeijingChina

Personalised recommendations