Entropy and the Uncertainty Principle

Rupert L. Frank; Elliott H. Lieb

doi:10.1007/s00023-012-0175-y

Entropy and the Uncertainty Principle

Rupert L. Frank
, Elliott H. Lieb

Mathematics

Research output: Contribution to journal › Article › peer-review

28 Scopus citations

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.

Original language	English (US)
Pages (from-to)	1711-1717
Number of pages	7
Journal	Annales Henri Poincare
Volume	13
Issue number	8
DOIs	https://doi.org/10.1007/s00023-012-0175-y
State	Published - Dec 2012

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Nuclear and High Energy Physics
Mathematical Physics

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10.1007/s00023-012-0175-y

Cite this

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title = "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.",

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T1 - Entropy and the Uncertainty Principle

AU - Frank, Rupert L.

AU - Lieb, Elliott H.

PY - 2012/12

Y1 - 2012/12

N2 - 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.

AB - 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.

UR - https://www.scopus.com/pages/publications/84868473495

UR - https://www.scopus.com/pages/publications/84868473495#tab=citedBy

U2 - 10.1007/s00023-012-0175-y

DO - 10.1007/s00023-012-0175-y

M3 - Article

AN - SCOPUS:84868473495

SN - 1424-0637

VL - 13

SP - 1711

EP - 1717

JO - Annales Henri Poincare

JF - Annales Henri Poincare

IS - 8

ER -

Entropy and the Uncertainty Principle

Abstract

All Science Journal Classification (ASJC) codes

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