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- W2117675594 abstract "It is shown that for any ensemble, whether classical or quantum, continuous or discrete, there is only one measure of the volume of the ensemble that is compatible with several basic geometric postulates. This volume measure is thus a preferred and universal choice for characterising the inherent spread, dispersion, localisation, etc, of the ensemble. Remarkably, this unique ensemble volume is a simple function of the ensemble entropy, and hence provides a new geometric characterisation of the latter quantity. Applications include unified, volume-based derivations of the Holevo and Shannon bounds in quantum and classical information theory; a precise geometric interpretation of thermodynamic entropy for equilibrium ensembles; a geometric derivation of semi-classical uncertainty relations; a new means for defining classical and quantum localization for arbitrary evolution processes; a geometric interpretation of relative entropy; and a new proposed definition for the spot-size of an optical beam. Advantages of the ensemble volume over other measures of localization (root-mean-square deviation, Renyi entropies, and inverse participation ratio) are discussed." @default.
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- W2117675594 date "1999-04-01" @default.
- W2117675594 modified "2023-10-08" @default.
- W2117675594 title "Universal geometric approach to uncertainty, entropy, and information" @default.
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- W2117675594 doi "https://doi.org/10.1103/physreva.59.2602" @default.
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