Not all states in the joint Hilbert space H A B 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 ψ A and ϕ ϕ A are both possible states for system A , and likewise ψ ψ B and ϕ ϕ B are both possible states for system B , then