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Logics for reasoning about quantum states and their evolution have been given in the literature. In this paper, we consider quantum computation tree logic (QCTL), which adds temporal modalities to exogenous quantum propositional logic. We give a sound and complete axiomatization of QCTL and combine the standard CTL model-checking algorithm with the dEQPL model-checking algorithm to obtain a model-checking algorithm for QCTL. Finally, we illustrate the use of the logic by reasoning about the BB84 key distribution protocol.

QUANTUM COMPUTATION TREE LOGIC — MODEL CHECKING AND COMPLETE CALCULUS