Entropic uncertainty and certainty relations for complementary observables

Abstract

The exact upper and lower bounds on the sum of the information entropies of three spin-1/2 operators SX, SY, SZ are derived. They show that, for a set of more than two observables, entropic uncertainty and certainty relations can exist which do not reduce to those satisfied by the pairs in the set. This result is generalized to sets of N+1 complementary observables existing in N-dimensional Hilbert spaces.