Discriminating N -qudit states using geometric structure
Donghoon Ha, Younghun Kwon · Physical Review A · 2014
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.