How do I write the general form of a 3 qubit mixed state ? It has 63 variables. Well one way is to use bloch vectors. So basically we take 3 single qubit mixed states (3 variables each) and tensor product them. Then we add the 2 qubit correlators and 3 qubit correlator terms. Finally we can divide it by its trace (to make its trace 1). It is hence unit trace and hermitian. However positive semidifinite condition is violated.