basis separable states product states
Not all states are separable states (and thus product states). Fix a basis 



{

|

i

⟩

A


}


{\displaystyle \{|i\rangle _{A}\}}

 for HA and a basis 



{

|

j

⟩

B


}


{\displaystyle \{|j\rangle _{B}\}}

 for HB. The most general state in HA ⊗ HB is of the form
