 Classically, an exclusive disjunction is true if and only if one of the disjuncts is true. Deutsch’s quantum circuit achieves its speed-up by exploiting the non-Boolean structure of quantum properties to efficiently distinguish between two disjunctive properties, without determining the truth values of the relevant disjuncts (representing the association of individual inputs to the function with corresponding outputs). The point of the procedure is to avoid the evaluation of the function for specific inputs in the determination of the global property, and it is this feature — impossible in the Boolean logic of classical computation — that leads to the speed-up relative to classical algorithms. (For quantum logic not specifically in relation to quantum computation, see the entry on  quantum logic and quantum probability).