  We demonstrate that the concept of information offers a more complete
description of complementarity than the traditional approach based on
observables. We present the first experimental test of information
complementarity for two-qubit pure states, achieving close agreement with
theory; We also explore the distribution of information in a comprehensive
range of mixed states. Our results highlight the strange and subtle properties
of even the simplest quantum systems: for example, entanglement can be
increased by reducing correlations between two subsystems.
