  The tensor product postulate of quantum mechanics states that the Hilbert
space of a composite system is the tensor product of the components' Hilbert
spaces. All current formalizations of quantum mechanics that do not contain
this postulate contain some equivalent postulate or assumption (sometimes
hidden). Here we give a natural definition of composite system as a set
containing the component systems and show how one can logically derive the
tensor product rule from the state postulate and from the measurement
postulate. In other words, our paper reduces by one the number of postulates
necessary to quantum mechanics.

Quantum Physics