Skip to main content
SpringerLink
Log in

Entanglement in Quantum Process Algebra

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

Abstract

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.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1

Similar content being viewed by others

References

  1. Baeten, J.C.M.: A brief history of process algebra. Theor. Comput. Sci. Process Algebra 335(2–3), 131–146 (2005)

    Article  MathSciNet  Google Scholar 

  2. Milner, R.: Communication and Concurrency. Prentice Hall (1989)

  3. Milner, R., Parrow, J., Walker, D.: A calculus of mobile processes, Parts I and II. Inf. Comput. 1992(100), 1–77 (1992)

    Article  Google Scholar 

  4. Hoare, C.A.R.: Communicating Sequential Processes. http://www.usingcsp.com/ (1985)

  5. Fokkink, W.: Introduction to Process Algebra, 2nd edn. Springer (2007)

  6. Plotkin, G.D.: A structural approach to operational semantics. Aarhus University, Tech Report DAIMIFN-19 (1981)

  7. Feng, Y., Duan, R.Y., Ji, Z.F., Ying, M.S.: Probabilistic bisimulations for quantum processes. Inf. Comput. 2007(205), 1608–1639 (2007)

    Article  MathSciNet  Google Scholar 

  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)

  9. Gay, S.J., Nagarajan, R.: Typechecking communicating quantum processes. Math. Struct. Comput. Sci. 2006(16), 375–406 (2006)

    Article  MathSciNet  Google Scholar 

  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)

  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. Lalire, M.: Relations among quantum processes: Bisimilarity and congruence. Math. Struct. Comput. Sci. 2006(16), 407–428 (2006)

    Article  MathSciNet  Google Scholar 

  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)

  14. Ying, M., Feng, Y., Duan, R., Ji, Z.: An algebra of quantum processes. ACM Trans. Comput. Logic (TOCL) 10(3), 1–36 (2009)

    Article  MathSciNet  Google Scholar 

  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)

  16. Ekert, A.K.: Quantum cryptography based on Bell’s theorem. Phys. Rev. Lett. 67(6), 661–663 (1991)

    Article  ADS  MathSciNet  Google Scholar 

  17. Deng, Y., Feng, Y.: Open bisimulation for quantum processes. Manuscript, arXiv:1201.0416 (2012)

  18. Feng, Y., Deng, Y., Ying, M.: Symbolic bisimulation for quantum processes. Manuscript, arXiv:1202.3484 (2012)

  19. Wang, Y.: An axiomatization for quantum processes to unifying quantum and classical computing. Manuscript, arXiv:1311.2960 (2013)

  20. Duncan, R.: Types for Quantum Computing. Ph.D. Dessertation, Oxford University (2006)

Download references

Author information

Authors and Affiliations

  1. College of Computer Science and Technology, Faculty of Information Technology, Beijing University of Technology, Beijing, 100124, China

    Yong Wang

Authors
  1. Yong Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yong Wang.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, Y. Entanglement in Quantum Process Algebra. Int J Theor Phys 58, 3611–3626 (2019). https://doi.org/10.1007/s10773-019-04226-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10773-019-04226-0

Keywords

Search

Navigation