We construct a formal framework for investigating epistemic and temporal notions in the context of distributed quantum computation. While we rely on structures developed in [1], we stress that our notion of quantum knowledge makes sense more generally in any agent-based model for distributed quantum systems. Several arguments are given to support our view that an agent’s possibility relation should not be based on the reduced density matrix, but rather on local classical states and local quantum operations. In this way, we are able to analyse distributed primitives such as superdense coding and teleportation, obtaining interesting conclusions as to how the knowledge of individual agents evolves. We show explicitly that the knowledge transfer in teleportation is essentially classical, in that eventually, the receiving agent knows that its state is equal to the initial state of the sender. The relevant epistemic statements for teleportation deal with this correlation rather than with the actual quantum state, which is unknown throughout the protocol.


Reduce Density Matrix Quantum Network Bell Measurement Superdense Code Computational Tree Logic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Danos, V., D’Hondt, E., Kashefi, E., Panangaden, P.: Distributed measurementbased quantum computation. In: Selinger, P. (ed.) Proceedings of the 3rd Workshop on Quantum Programming Languages, QPL 2005 (2005)Google Scholar
  2. 2.
    Hintikka, J.: Knowledge and belief - An introduction to the logic of the two notions. Cornell University Press, Ithaca (1962)Google Scholar
  3. 3.
    Halpern, J.Y.: Reasoning about knowledge: a survey. In: Handbook of Logic in Artificial Intelligence and Logic Programming., vol. 4, pp. 1–34. Oxford University Press, Oxford (1995)Google Scholar
  4. 4.
    Fagin, R., Halpern, J.Y., Moses, Y., Vardi, M.Y.: Reasoning about knowledge. MIT Press, Cambridge (1995)zbMATHGoogle Scholar
  5. 5.
    Nielsen, M.A., Chuang, I.: Quantum computation and quantum information. Cambridge University Press, Cambridge (2000)zbMATHGoogle Scholar
  6. 6.
    Baltag, A., Smets, S.: Quantum dynamic logic. In: Selinger, P. (ed.) Proceedings of the 2nd Workshop on Quantum Programming Languages (QPL 2004), Turku, Finland, Turku Centre for Computer Science, TUCS General Publication No 33 (2004)Google Scholar
  7. 7.
    Baltag, A., Smets, S.: LQP: the dynamic logic of quantum information (2005) (unpublished)Google Scholar
  8. 8.
    van der Meyden, R., Patra, M.: A logic for probability in quantum systems. In: Proc. Computer Science Logic and 8th Kurt Gödel Colloquium, Vienna, Austria, pp. 427–440 (2003)Google Scholar
  9. 9.
    van der Meyden, R., Patra, M.: Knowledge in quantum systems. In: Proceedings of the 9th conference on Theoretical aspects of rationality and knowledge, Bloomington, Indiana, pp. 104–117 (2003)Google Scholar
  10. 10.
    Danos, V., Kashefi, E., Panangaden, P.: The measurement calculus. quantph/ 0412135 (2004)Google Scholar
  11. 11.
    D’Hondt, E.: Distributed quantum computation – A measurement-based approach. Ph.D. thesis, Vrije Universiteit Brussel (2005) (in preparation)Google Scholar
  12. 12.
    Emerson, E.A.: Temporal and modal logic. In: Handbook of Theoretical Computer Science. Formal Models and Sematics (B), vol. B, pp. 995–1072. MIT Press, Cambridge (1990)Google Scholar
  13. 13.
    Bennett, C.H., Wiesner, S.J.: Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states. Phys. Rev. Lett., 2881–2884 (1992)Google Scholar
  14. 14.
    Bennett, C.H., Brassard, G., Crépeau, C., Jozsa, R., Peres, A., Wootters, W.: Teleporting an unknown quantum state via dual classical and EPR channels. Phys. Rev. Lett. 70, 1895–1899 (1993)zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    D’Hondt, E., Panangaden, P.: The computational power of the W and GHZ states. Journal on Quantum Information & Computation (2005) (to appear)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Ellie D’Hondt
    • 1
  • Prakash Panangaden
    • 2
  1. 1.Vrije Universiteit BrusselBelgium
  2. 2.McGill UniversityCanada

Personalised recommendations