Un approccio categoriale ai flussi di informazione quantistica

In strongly compact closed category with biproducts many crucial features of quantum computing in Hilbert spaces have been recently recasted: the additive level describes the irreversible process of measure and allows to model the classical information flow during a quantum information protocol. In this paper we suggest to grasp the different situations occurring in quantum information theory where the input output systems of an information channel can be either quantum or classical only on the base of the multiplicative level of the category. The aim of our approach is not restricted to a formalization of the standard Hilbert space point of view, but intends to gain a more operational meaning. More precisely, we analyze the conditions on the monoids of the category which allow to recover a categorical version of the notion of C*-algebras acting on a Hilbert space and which will be subject to a precise valutation regarding the no-cloning principle. We find that the elements of the monoid invariant with respect to the action of the cloning form exactly a commutative subalgebra, the categorical structure for a classical object.