Quantum Probabilistic Dyadic Second-Order Logic

  • Alexandru Baltag
  • Jort M. Bergfeld
  • Kohei Kishida
  • Joshua Sack
  • Sonja J. L. Smets
  • Shengyang Zhong
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8071)

Abstract

We propose an expressive but decidable logic for reasoning about quantum systems. The logic is endowed with tensor operators to capture properties of composite systems, and with probabilistic predication formulas P ≥ r (s), saying that a quantum system in state s will yield the answer ‘yes’ (i.e. it will collapse to a state satisfying property P) with a probability at least r whenever a binary measurement of property P is performed. Besides first-order quantifiers ranging over quantum states, we have two second-order quantifiers, one ranging over quantum-testable properties, the other over quantum “actions”. We use this formalism to express the correctness of some quantum programs. We prove decidability, via translation into the first-order logic of real numbers.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Alexandru Baltag
    • 1
  • Jort M. Bergfeld
    • 1
  • Kohei Kishida
    • 1
  • Joshua Sack
    • 1
  • Sonja J. L. Smets
    • 1
  • Shengyang Zhong
    • 1
  1. 1.Institute for Logic, Language and ComputationUniversiteit van AmsterdamAmsterdamThe Netherlands

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