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The provision of optimal entanglement on underlying networks of group association schemes

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