Entropy and the Uncertainty Principle

Abstract

We generalize, improve and unify theorems of Rumin, and Maassen-Uffink about classical entropies associated with quantum density matrices. These theorems refer to the classical entropies of the diagonals of a density matrix in two different bases. Thus, they provide a kind of uncertainty principle. Our inequalities are sharp because they are exact in the high-temperature or semi-classical limit. © 2012 The Author(s).