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Entropy and the Uncertainty Principle

Frank, Rupert L. and Lieb, Elliott H. (2012) Entropy and the Uncertainty Principle. Annales Henri Poincaré, 13 (8). pp. 1711-1717. ISSN 1424-0637. doi:10.1007/s00023-012-0175-y.

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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.

Item Type:Article
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URLURL TypeDescription Paper ReadCube access
Frank, Rupert L.0000-0001-7973-4688
Lieb, Elliott H.0000-0001-5843-3587
Additional Information:© 2012 The Author. This paper may be reproduced, in its entirety, for noncommercial purposes. The work was partially supported by NSF Grants PHY-1068285 (R.L.F.) and PHY-0965859 (E.H.L.).
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Issue or Number:8
Record Number:CaltechAUTHORS:20170501-103316603
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Official Citation:Frank, R.L. & Lieb, E.H. Ann. Henri Poincaré (2012) 13: 1711. doi:10.1007/s00023-012-0175-y
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:77103
Deposited By: Ruth Sustaita
Deposited On:01 May 2017 18:41
Last Modified:15 Nov 2021 17:28

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