Optimal Entanglement Provision over Underlying Networks of Group Association Schemes

We investigate creation of optimal entanglement in symmetric networks. The proposed network is one in which the connections are organized by a group table in other words a group association scheme. We show that optimal entanglement can be provided over such networks by adjusting couplings and initial state. We find that the optimal initial state is a simple local excited state. Moreover we obtain an analytic formula for entanglement achievable between vertex pairs located in the same strata and calculate their relevant optimal couplings. For those pairs located in different strata two upper bounds are presented. These results are also checked numerically.