Joonwoo Bae, Won-Young Hwang
We show a geometric formulation for qubit state discrimination, that can be generally applied, and provide the complete solution in a closed form when arbitrary qubit states are given with equal a priori probabilities. It is shown that the guessing probability does not depend on detailed relations among given states, such as angles between them, but on a property that can be assigned by the set of given states itself. This also shows how a set of quantum states can be modified such that they give the same guessing probability. The general structure of optimal measurements is characterized, which also explains that no measurement sometimes gives an optimal strategy.
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http://arxiv.org/abs/1204.2313
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