A New Connective in Natural Deduction, and its Application to Quantum Computing
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We investigate an unsuspected connection between non harmonious logical connectives, such as Prior's tonk, and quantum computing. We defend the idea that non harmonious connectives model the information erasure, the non-reversibility, and the non-determinism that occur, among other places, in quantum measurement. More concretely, we introduce a propositional logic with a non harmonious connective sup, prove cut elimination for this logic, and show that its proof language forms the core of a quantum programming language.
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