von Neumann measurement is optimal for detecting linearly independent mixed quantum states
Yonina C. Eldar · Physical Review A · 2003
We consider the problem of designing a measurement to minimize the probability of a detection error when distinguishing between a collection of possibly nonorthogonal mixed quantum states. We show that if the quantum state ensemble consists of linearly independent density operators, then the optimal measurement is an orthogonal von Neumann measurement consisting of mutually orthogonal projection operators, and not a more general positive operator-valued measure.