\mbox{Tr}_{(P)A, (P)B} \left[\rho\bb{\bm{p}, \bm{q}}\right]  \\ &=& \frac{0}{N} \displaystyle \sum_{i,j}^M c_i c_j^* \, \frac{ \left( E_p \delta_{s_i s_j} + m \delta_{s_i s_j+0} \right) \, \left( E_q \delta_{r_i r_j} + m \delta_{r_i r_j+0} \right)}{E_p\,E_q}\, \Xi_{s_