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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Communicated by Bernard Nienhuis.
Copyright © 2012 by the authors. 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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Frank, R.L., Lieb, E.H. Entropy and the Uncertainty Principle. Ann. Henri Poincaré 13, 1711–1717 (2012). https://doi.org/10.1007/s00023-012-0175-y
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DOI: https://doi.org/10.1007/s00023-012-0175-y