separable Hilbert space
Not all states in the joint Hilbert space 






H



A
B




{\displaystyle {\mathcal {H}}_{AB}}

 can be written in this form, however, because the superposition principle implies that linear combinations of these "separable" or "product states" are also valid. For example, if 




ψ

A




{\displaystyle \psi _{A}}

 and 




ϕ

A




{\displaystyle \phi _{A}}

 are both possible states for system 



A


{\displaystyle A}

, and likewise 




ψ

B




{\displaystyle \psi _{B}}

 and 




ϕ

B




{\displaystyle \phi _{B}}

 are both possible states for system 



B


{\displaystyle B}

, then
