Entropy and the Uncertainty Principle

被引：0

作者：

Rupert L. Frank

Elliott H. Lieb

机构：

[1] Princeton University,Department of Mathematics

[2] Princeton University,Departments of Mathematics and Physics

来源：

Annales Henri Poincaré | 2012年 / 13卷

关键词：

Entropy; Density Matrix; Discrete Fourier Transform; Uncertainty Principle; Trace Class;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

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.

引用

页码：1711 / 1717

页数：6

共 7 条

[1] Beckner W.(1975)Inequalities in Fourier analysis Ann. Math. (2) 102 159-182
[2] Deutsch D.(1983)Uncertainty in quantum measurements Phys. Rev. Lett. 50 631-633
[3] Hirschman I.I.(1957)A note on entropy Am. J. Math. 79 152-156
[4] Kraus K.(1987)Complementary observables and uncertainty relations Phys. Rev. D 35 3070-3075
[5] Maassen H.(1988)Generalized entropic uncertainty relations Phys. Rev. Lett. 60 1103-1106
[6] Uffink J.B.M.(2011)Balanced distribution-energy inequalities and related entropy bounds Duke Math. J. 160 567-597
[7] Rumin M.(undefined)undefined undefined undefined undefined-undefined

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