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Complementarity polytope is a geometric structure that exists in N2-1dimensional space for an N dimensional Hilbert space. The existence of N + 1mutually unbiased bases(MUBs) is possible, if such a polytope can be shown tobe a subset of density matrices, which is a very difficult task. With the hopeof simplifying this task, we have shown in this work that, the complementaritypolytope can be characterized by the total extractable information from N+1MUBs. We also demonstrate that t less than (N+1) number of MUBs also form apolytope that exists in t(N-1) dimensional space, which we refer to asgeneralized complementarity polytope. The generalized complementarity polytopecan also be characterized by total extractable information from t MUBs.

Characterizing the generalized complementarity polytope with extractable information from MUBs