We study the question of how highly entangled two particles can be when also entangled in a similar way with other particles on the complete graph Kn for the case of Werner, isotropic and Brauer states. We formalize our question as a semidefinite program and then solve this optimization problem analytically, using tools from representation theory. In particular, we determine the exact maximum values p of the projection to the maximally entangled state and antisymmetric Werner state possible, solving long-standing open problems. This is joint work with Rene Allerstorfer, Matthias Christandl, Dmitry Grinko, Maris Ozols, Denis Rochette, and Philip Verduyn Lunel, arXiv:2309.16655
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