Two linearities for quantum computing in the lambda calculus
Abstract
We propose a way to unify two approaches of noncloning in quantum lambdacalculi: logical and algebraic linearities. The first approach is to forbid duplicating variables, while the second is to consider all lambdaterms as algebraiclinear functions. We illustrate this idea by defining a quantum extension of firstorder simplytyped lambdacalculus, 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 nonsuperposed types as their basis.
 Publication:

arXiv eprints
 Pub Date:
 January 2016
 arXiv:
 arXiv:1601.04294
 Bibcode:
 2016arXiv160104294D
 Keywords:

 Computer Science  Logic in Computer Science
 EPrint:
 Long journal version of TPNC'17 paper (doi:10.1007/9783319710693_22) extended with third author's "Licenciatura"'s thesis