 the coincidence set ${\rm {\mathcal S}}_{R_{j} }^{\left(\pi _{S} \right)} \left(\left(R_{i} ,\sigma _{k} \right)\right)$ is a subset of incoming density matrices in ${\rm {\mathcal S}}_{I} \left(R_{j} \right)$ of $R_{j} $ received from $R_{i} $ that requires the outgoing density matrix $\sigma _{k} $ from ${\rm {\mathcal S}}_{O} \left(R_{j} \right)$ for the entanglement swapping. 