Annales Henri Poincaré

, Volume 13, Issue 8, pp 1711–1717 | Cite as

Entropy and the Uncertainty Principle

  • Rupert L. Frank
  • Elliott H. Lieb


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.


Entropy Density Matrix Discrete Fourier Transform Uncertainty Principle Trace Class 
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Copyright information

© The Author(s) 2012

Authors and Affiliations

  1. 1.Department of MathematicsPrinceton UniversityPrincetonUSA
  2. 2.Departments of Mathematics and PhysicsPrinceton UniversityPrincetonUSA

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