1 qubit can be expressed as 1/2(I + n.σ). where n = (n_x,n_y,n_z) is a 3D vector, with size <=1. Hence the condition is that the sum of squares of the variables must be 1 or less. In the general expression of multi-qubit systems, we tensor product these individual qubits and also add the correlator terms. For example a 3 qubit general state will have 63 variables. The question is what are the conditions on these variables in order for it to be a valid density matrix ?