Discriminating N-qudit states using geometric structure

Abstract

Quantum state discrimination is a fundamental task having many applications in quantum information processing. However up to now there has been no rigorous formulation for discriminating N-qudit states. In this article we provide a geometric method to obtain minimum error discrimination for N-qudit states. By using the geometric approach to minimum-error discrimination for N-qudit states, we supply the condition for the existence of optimal measurement that can be composed of null operators, which gives a key understanding for discriminating N-qudit states. Furthermore we present how the number of nonzero operators for optimal measurement can be reduced. Applying our method to symmetric N-qudit states we obtain optimal measurements, which are different from known ones.