Quantum Control in the Unitary Sphere: Lambda-S1 and its Categorical Model

In a recent paper, realizability technique has been used to give semantics of quantum lambda calculus. Such gives rise an infinite number valid typing rules, without giving preference any subset those. this we introduce defining expressive enough Then, propose categorical for it. consists adjunction between the category distributive-action spaces value distributions (that is, linear combinations values in calculus), and sets distributions.