The above description does not seem accurate -- the arrows should be *unitary* transformations or *contractions.* Otherwise, this is none other than the category of finite dimensional vector spaces.
- Actually, I added 'between them' thus, it must satisfies some properties w.r.t. the form. This (unitary maps or contraction) should be added in the 'properties' list and defined w.r.t. the dagger-monoidal structure. Moreover, discussion should *not* take place in the article but here.