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Pramana

On the discretization of probability density functions and the continuous Rényi entropy

Diógenes Campos

Published Jul 18, 2015• 2 citations
Publisher
DOI
10.1007/s12043-015-0955-2

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In this paper we study multipartite and correlated majorization of the finite discrete probability distributions emerging in quantum information theory. We start proving the subadditivity of the Rényi and Burg entropies, and we show that the criteria for such a generalized majorization scheme can be provided solely in terms of the Rényi and Burg entropies. Surprisingly, the same set of criteria applies both to the correlated and uncorrelated cases. Finally, based on our findings in majorization, we give a proof of the characterization of the Rényi and Burg entropies in terms of continuity, symmetry and (sub)additivity.
Majorization effect on some entropic functionals, such as von-Neumann, Shannon, atomic Wehrl and Rényi entropies are investigated of a V-type three-level atom, which interacts with a coherent field in a resonant cavity. Fidelity, purity and linear entropy are investigated for two quantum systems, which contain photon number distributions and Husimi Q functions. A relation between majorization and localization properties of continuous density functionals is established. The results are compared and verified for continuous and discrete distributions of an atom-field interacting system.