Advertisement

International Journal of Theoretical Physics

, Volume 56, Issue 12, pp 3991–4003 | Cite as

A Logical Analysis of Quantum Voting Protocols

  • Soroush Rafiee Rad
  • Elahe Shirinkalam
  • Sonja Smets
Article
  • 96 Downloads

Abstract

In this paper we provide a logical analysis of the Quantum Voting Protocol for Anonymous Surveying as developed by Horoshko and Kilin in (Phys. Lett. A 375, 1172–1175 2011). In particular we make use of the probabilistic logic of quantum programs as developed in (Int. J. Theor. Phys. 53, 3628–3647 2014) to provide a formal specification of the protocol and to derive its correctness. Our analysis is part of a wider program on the application of quantum logics to the formal verification of protocols in quantum communication and quantum computation.

Keywords

Dynamic quantum logic Quantum voting protocol Protocol verification 

References

  1. 1.
    Baltag, A., Smets, S.: The Logic of Quantum Programs The proceedings of the 2nd International Workshop on Quantum Programming Languages (QPL), TUCS General Publication, vol. 33 (2004)Google Scholar
  2. 2.
    Baltag, A., Smets, S.: LQP: The Dynamic logic of quantum information. Mathematical Structures in Computer Science, Special Issue on Quantum Programming Languages 16(3), 491–525 (2006)CrossRefMATHMathSciNetGoogle Scholar
  3. 3.
    Baltag, A., Smets, S.: Complete axiomatizations for quantum actions. Int. J. Theor. Phys. 44(12), 2267–2282 (2005)CrossRefMATHMathSciNetGoogle Scholar
  4. 4.
    Baltag, A, Smets, S.: A Dynamic - Logical Perspective on Quantum Behavior, Studia Logica. In: Douven, I., Horsten, L. (eds.) Special issue on Applied Logic in the Philosophy of Science, vol. 89, pp. 185–209 (2008)Google Scholar
  5. 5.
    Baltag, A., Smets, S.: Quantum Logic as a Dynamic Logic, Synthese. In: Kuipers, T., van Benthem, J., Visser, H. (eds.) Special issue (2011)Google Scholar
  6. 6.
    Baltag, A., Smets, S: The Dynamic Turn in Quantum Logic. Synthese 186(3) (2012)Google Scholar
  7. 7.
    Baltag, A., Bergfeld, J., Kishida, K., Smets, S., Sack, J., Zhong, S.: PLQP & Company: Decidable Logics for Quantum Algorithms. Int. J. Theor. Phys. 53 (10), 3628–3647 (2014)CrossRefMATHMathSciNetGoogle Scholar
  8. 8.
    Baltag, A., Smets, S.: Correlated knowledge, an Epistemic-Logic view on quantum entanglement. Int. J. Theor. Phys. 49 (2010)Google Scholar
  9. 9.
    Baltag, A., Smets, S.: Modeling correlated information change: from conditional beliefs to quantum conditionals. Soft. Comput. 21, 1523–1535 (2017)CrossRefGoogle Scholar
  10. 10.
    Beltrametti, E., Dalla Chiara, M.L., Giuntini, R, Leporini, R., Sergioli, G.: Epistemic quantum computational structures in a Hilbert-space environment. Fundam Inf 115, 1–14 (2012)MATHMathSciNetGoogle Scholar
  11. 11.
    Beltrametti, E., Dalla Chiara, M.L., Giuntini, R., Sergioli, G.: Quantum teleportation and quantum epistemic semantics. Math Slovacca 62(6), 1–24 (2012)ADSMATHMathSciNetGoogle Scholar
  12. 12.
    Beltrametti, E., Dalla Chiara, M.L., Giuntini, R., Leporini, R., Sergioli, G.: A quantum computational semantics for epistemic logical operators. Part I: epistemic structures. Int. J. Theor. Phys. 53(10), 3279–3292 (2014)CrossRefMATHMathSciNetGoogle Scholar
  13. 13.
    Bergfeld, J.M., Sack, J.: Deriving the correctness of quantum protocols in the probabilistic logic for quantum programs. Soft. Comput. 21(6), 1421–1441 (2017)CrossRefGoogle Scholar
  14. 14.
    Birkhoff, G., von Neumann, J.: The Logic of Quantum Mechanics. Ann. Math. 37, 823–843 (1936). reprinted in Hooker, C.A. (ed.), The Logico-algebraic Approach to Quantum Mechanics, vol 1: p.1–26, (1975)CrossRefMATHMathSciNetGoogle Scholar
  15. 15.
    Dolev, S h, Pitowsky, B.: A quantum secret ballot, coRR abs/quant-ph/0602087 (2006)Google Scholar
  16. 16.
    Horoshko, D., Kilin, S.: Quantum anonymous voting with anonymity check. Phys. Lett. A 375, 1172–1175 (2011)ADSCrossRefMATHMathSciNetGoogle Scholar
  17. 17.
    Inamon, H., Lutkenhaus, N., Mayers, D.: Unconditional security of practical quantum key disribution. Eur. Phys. J. D 41(3), 599–627 (2007)ADSCrossRefGoogle Scholar
  18. 18.
    Sergioli, G., Leporini, R.: Quantum approach to epistemic semantics. Soft. Comput. 21 (2017)Google Scholar

Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Institute for Logic, Language and ComputationUniversity of AmsterdamAmsterdamNetherlands
  2. 2.Department of MathematicsShahid Beheshti UniversityTehranIran

Personalised recommendations