Typing Quantum Superpositions and Measurement

Abstract : We propose a way to unify two approaches of non-cloning in quantum lambda-calculi. The first approach is to forbid duplicating variables, while the second is to consider all lambda-terms as algebraic-linear functions. We illustrate this idea by defining a quantum extension of first-order simply-typed lambda-calculus, where the type is linear on superposition, while allows cloning base vectors. In addition, we provide an interpretation of the calculus where superposed types are interpreted as vector spaces and non-superposed types as their basis.
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Alejandro Díaz-Caro, Gilles Dowek. Typing Quantum Superpositions and Measurement. TPNC 2017 - 6th International Conference on the Theory and Practice of Natural Computing, Dec 2017, Prague, Czech Republic. pp.13, ⟨10.1007/978-3-319-71069-3_22⟩. ⟨hal-01670387⟩

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