Local measurements are sufficient to obtain maximal information on independently prepared quantum states

Abstract

Given a composite quantum system in which the states of the subsystems are independently (but not necessarily identically) prepared, we construct separate measurements on the subsystems from any given joint measurement such that the former always give at least as much information as the latter. This construction offers insights into the understanding of measurements on this type of composite system. Moreover, this construction essentially proves the intuition that separate measurements on the subsystems are sufficient to extract the maximal information about the separately prepared subsystems, thus making a joint measurement unnecessary. Furthermore, our result implies that individual attacks are as powerful as collective attacks in obtaining information about the raw key in quantum key distribution.