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Temporal logics for reasoning about quantum systems

Reasoning about quantum systems has gained prominence due to a big potential in applications such as information processing, security, distributed systems and randomized algorithms. This fact has attracted research in formal reasoning about quantum states, programs and processes. On the other hand, temporal logics have proved to be successful in the verification of classical distributed systems and security protocols. In this chapter we extend Exogenous Quantum Propositional Logic with temporal modalities, considering both linear and branching time. We provide a weakly complete Hilbert calculi for the proposed quantum temporal logics and study their SAT and model-checking problems.