A new connective in natural deduction, and its application to quantum computing

Authors: Alejandro Díaz-Caro, Gilles Dowek.

Abstract: We investigate an unsuspected connection between logical connectives with non-harmonious deduction rules, such as Prior’s tonk, and quantum computing. We argue that these connectives model the information-erasure, the non-reversibility, and the non-determinism that occur, among other places, in quantum measurement. We introduce an intuitionistic propositional logic with a non-harmonious logical connective sup and two interstitial rules, and show that the proof language of this logic forms the core of a quantum programming language.

More information:
https://www.sciencedirect.com/science/article/abs/pii/S0304397523001536