Complementarity and correlations

Lorenzo Maccone, Dagmar Bruss, Chiara Macchiavello

Published 2014-08-28Version 1

We investigate the relation between complementary properties and correlations of composite quantum systems. We introduce three measures of correlations which are based on local measurements in complementary bases. These measures are linked to the mutual information, the Pearson correlation coefficient and the sum of conditional probabilities, respectively. We show that states which have complementary correlations beyond a certain threshold must be entangled. The reverse is not true, however. We also show that, surprisingly, states with non-zero quantum correlations may have less correlations on complementary observables than classically correlated states.