On the completeness of quantum computation models

The notion of computability is stable (i.e. independent of the choice of an indexing) over infinite-dimensional vector spaces provided they have a finite "tensorial dimension". Such vector spaces with a finite tensorial dimension permit to define an absolute notion of completeness for quantum computation models and give a precise meaning to the Church-Turing thesis in the framework of quantum theory. (Extra keywords: quantum programming languages, denotational semantics, universality.)