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

Abstract

In this work, we provide a complete analysis to minimum-error discrimination of mixed four qubit states with arbitrary prior probabilities. For the complete analysis, the most important work to do is to find the necessary and sufficient conditions for the existence of null measurement operator. From the geometric structure of qubit states, we obtain the analytic condition for deciding the existence of a null operator in minimum-error measurement for four mixed qubit states, which also gives the necessary and sufficient conditions for every optimal POVM to have nonzero elements. Using the condition, we completely analyze minimum-error discrimination of four mixed qubit states with arbitrary prior probabilities. © 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.