International Journal of Theoretical Physics

, Volume 53, Issue 10, pp 3628–3647 | Cite as

PLQP & Company: Decidable Logics for Quantum Algorithms

  • Alexandru Baltag
  • Jort Bergfeld
  • Kohei Kishida
  • Joshua Sack
  • Sonja Smets
  • Shengyang Zhong


We introduce a probabilistic modal (dynamic-epistemic) quantum logic PLQP for reasoning about quantum algorithms. We illustrate its expressivity by using it to encode the correctness of the well-known quantum search algorithm, as well as of a quantum protocol known to solve one of the paradigmatic tasks from classical distributed computing (the leader election problem). We also provide a general method (extending an idea employed in the decidability proof in Dunn et al. (J. Symb. Log. 70:353–359, 2005)) for proving the decidability of a range of quantum logics, interpreted on finite-dimensional Hilbert spaces. We give general conditions for the applicability of this method, and in particular we apply it to prove the decidability of PLQP.


Quantum logic Modal logic Quantum computation Decidability 


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Alexandru Baltag
    • 1
  • Jort Bergfeld
    • 1
  • Kohei Kishida
    • 2
  • Joshua Sack
    • 1
  • Sonja Smets
    • 1
  • Shengyang Zhong
    • 1
  1. 1.ILLCUniversity of AmsterdamAmsterdamThe Netherlands
  2. 2.Department of Computer ScienceUniversity of OxfordOxfordUK

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