Generalization of quantum-state comparison
Matthias Kleinmann, Hermann Kampermann, Dagmar Bruß · Physical Review A · 2005
We investigate the unambiguous comparison of quantum states in a scenario that is more general than the one that was originally suggested by Barnett et al. First, we find the optimal solution for the comparison of two states taken from a set of two pure states with arbitrary a priori probabilities. We show that the optimal coherent measurement is always superior to the optimal incoherent measurement. Second, we develop a strategy for the comparison of two states from a set of $N$ pure states, and find an optimal solution for some parameter range when $N=3$. In both cases we use the reduction method for the corresponding problem of mixed-state discrimination, as introduced by Raynal et al., which reduces the problem to the discrimination of two pure states only for $N=2$. Finally, we provide a necessary and sufficient condition for unambiguous comparison of mixed states to be possible.