
handle: 11336/42228
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.
LAMBDA CALCULUS, [INFO.INFO-LO] Computer Science [cs]/Logic in Computer Science [cs.LO], lambda-calculus, quantum computing, QUANTUM COMPUTING, algebraic linearity, ALGEBRAIC LINEARITY, linear logic, https://purl.org/becyt/ford/1.2, measurement, https://purl.org/becyt/ford/1, LINEAR LOGIC
LAMBDA CALCULUS, [INFO.INFO-LO] Computer Science [cs]/Logic in Computer Science [cs.LO], lambda-calculus, quantum computing, QUANTUM COMPUTING, algebraic linearity, ALGEBRAIC LINEARITY, linear logic, https://purl.org/becyt/ford/1.2, measurement, https://purl.org/becyt/ford/1, LINEAR LOGIC
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