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. © 1995 The American Physical Society.