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Annales Henri Poincare, Vol. 13, No. 8. (1 December 2012), pp. 1711-1717, doi:10.1007/s00023-012-0175-y Key: citeulike:10520020
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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.
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