Entropy and the Uncertainty Principle

Rupert L. Frank, Elliott H. Lieb

Research output: Contribution to journalArticlepeer-review

22 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)1711-1717
Number of pages7
JournalAnnales Henri Poincare
Issue number8
StatePublished - Dec 2012

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Nuclear and High Energy Physics
  • Mathematical Physics


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