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Physica Scripta

Tomographic Rényi entropy of multimode Gaussian states

Margarita A. Man’ko

Published Feb 11, 2013• 3 citations
Publisher

Abstract

The Rényi and Shannon entropies associated with optical and symplectic tomograms of multimode photon states are obtained in explicit form. Some new inequalities for the tomographic entropies are studied.
DOI
10.1088/0031-8949/87/03/038113

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The probability distribution determining the quantum states of photons and qudits are reviewed. Shannon, Rényi and Tsallis entropies associated with the probability distributions are discussed. Shannon information associated with quantum states in the probability representation is considered. Known inequalities for the classical joint probability distributions determining quantum states of multipartite systems are discussed in detail and the relationship to the inequalities known for quantum von Neumann entropy of the states is presented. Properties of subadditivity and strong subadditivity of the von Neumann entropy of two-partite and multipartite qudit states are considered in view of the subadditivity and strong subadditivity properties of Shannon entropies associated with classical joint probability distributions determining the multiqudit quantum states. The new entropic uncertainty relationships for optical tomograms are suggested as a test for accuracy of the homodyne reconstructing the photon state.