We show a geometric formulation for minimum-error discrimination of qubitstates, that can be applied to arbitrary sets of qubit states given witharbitrary a priori probabilities. In particular, when qubit states are givenwith equal \emph{a priori} probabilities, we provide a systematic way offinding optimal discrimination and the complete solution in a closed form. Thisgenerally gives a bound to cases when prior probabilities are unequal. Then, itis shown that the guessing probability does not depend on detailed relationsamong given states, such as angles between them, but on a property that can beassigned by the set of given states itself. This also shows how a set ofquantum states can be modified such that the guessing probability remains thesame. Optimal measurements are also characterized accordingly, and a generalmethod of finding them is provided.
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