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In this work, we provide a complete analysis to minimum-error discriminationof mixed four qubit states with arbitrary prior probabilities. For the completeanaysis, the most important work to do is to find the necessary and sufficientconditions for the existence of null measurement operator. From the geometricstructure of qubit states, we obtain the analytic condition for deciding theexistence of a null operator in minimum-error measurement for mixed four qubitstates, which also gives the necessary and sufficient conditions for everyoptimal POVM to have non-zero elements. Using the condition, we completelyanalyze minimum-error discrimination of mixed four qubit states with arbitraryprior probabilities.

Complete analysis to minimum-error discrimination of mixed four qubit states with arbitrary prior probabilities