ua nt - p h / 98 08 00 9 v 1 5 A ug 1 99 8 An Example of Non - Attainability of Expected Quantum Information

Braunstein and Caves showed how quantum information can be used to define a metric for quantum states, relying on attainability of a quantum information bound. We show that the bound is not generally attainable. But a two-stage procedure of repeated measurements achieves the bound in the limit. We connect to the question of whether a generalised measurement on n independent copies of a quantum system can yield more information than n separate measurements. Separate measurements are in the limit as informative as joint, and measurement of classical observables suffices.