 for a given entanglement swapping $\zeta \left(\pi _{S} \right)$ at a given $\pi _{S} $, as $$\label{00)}  \begin{split}    \omega \left( {{\pi }_{S}} \right)&=\sum\limits_{i,k}{{{\zeta }_{ik}}\left( {{\rho }_{A}},{{\sigma }_{k}} \right)Z_{{{R}_{j}}}^{\left( {{\pi }_{S}} \right)}\left( \left( {{R}_{i}},{{\sigma }_{k}} \right) \right)} \\   & =\left\langle \