Optimal Extraction of Information from Finite Quantum Ensembles

Given only a finite ensemble of identically prepared particles, how precisely can one determine their states? We describe optimal measurement procedures in the case of spin $1/2$ particles. Furthermore, we prove that optimal measurement procedures must necessarily view the ensemble as a single composite system rather than as the sum of its components, i.e., optimal measurements cannot be realized by separate measurements on each particle.

Optimal Extraction of Information from Finite Quantum Ensembles | Litlas