  Uncertainty principle, a fundamental principle in quantum physics, has been
studied intensively via various uncertainty inequalities. Here we derive an
uncertainty equality in terms of linear entropy, and show that the sum of
uncertainty in complementary local bases is equal to a fixed quantity. We also
introduce a measure of correlation in a bipartite state, and show that the sum
of correlations revealed in a full set of complementary bases is equal to the
total correlation in the bipartite state. The surprising simple equality
relations we obtain imply that the study on uncertainty principle and
correlations can rely on the use of linear entropy, a simple quantity that is
very convenient for calculation.
