Hi, i've seen the following in quantum info textbooks and papers and I was just wondering if anyone knows if it has any phsical interpretation or significance? The space of operators that act on a HIlbert space is isomorphic to the tensor product of the original Hilbert space with its dual: H otimes H* ~ L(H) This means that if we start with a tensor product Hilbert space then it is possible to regard the states in this space as operators acting on another space. I.e. there is a one-to-one relationship between the vectors of this tensor product space and operators acting on a seperate space. Ok, the axioms of QM require that the tensor product be used when the system has more than one degree of freedom. Does this then mean that perhaps composite quantum systems in certain states can be imagined as acting as observables on other quantum systems? What do you guys think? Am I reading too much into it?