An example of non-attainability of expected quantum information

Abstract

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 that a two-stage procedure of repeated measurements achieves the bound in the limit. We connect to the question of ' non-locality without entanglement'; can a joint measurement on n independent copies of a quantum system yield more information than separate measurements. Though for small n generalized measurements are more informative, the gain is asymptotically negligible in the pure state, spin-half, examples studied.