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• W2034306513 abstract "Jensen-Shannon divergence (JD) is a symmetrized and smoothed version of the most important divergence measure of information theory, Kullback divergence. As opposed to Kullback divergence it determines in a very direct way a metric; indeed, it is the square of a metric. We consider a family of divergence measures (${text{JD}}_{ensuremath{alpha}}$ for $ensuremath{alpha}>0$), the Jensen divergences of order $ensuremath{alpha}$, which generalize JD as ${text{JD}}_{1}=text{JD}$. Using a result of Schoenberg, we prove that ${text{JD}}_{ensuremath{alpha}}$ is the square of a metric for $ensuremath{alpha}∊(0,2]$, and that the resulting metric space of probability distributions can be isometrically embedded in a real Hilbert space. Quantum Jensen-Shannon divergence (QJD) is a symmetrized and smoothed version of quantum relative entropy and can be extended to a family of quantum Jensen divergences of order $ensuremath{alpha}$ $({text{QJD}}_{ensuremath{alpha}})$. We strengthen results by Lamberti and co-workers by proving that for qubits and pure states, ${text{QJD}}_{ensuremath{alpha}}^{1/2}$ is a metric space which can be isometrically embedded in a real Hilbert space when $ensuremath{alpha}∊(0,2]$. In analogy with Burbea and Rao's generalization of JD, we also define general QJD by associating a Jensen-type quantity to any weighted family of states. Appropriate interpretations of quantities introduced are discussed and bounds are derived in terms of the total variation and trace distance." @default.
• W2034306513 created "2016-06-24" @default.
• W2034306513 creator A5021606672 @default.
• W2034306513 creator A5036626877 @default.
• W2034306513 date "2009-05-12" @default.
• W2034306513 modified "2023-10-03" @default.
• W2034306513 title "Properties of classical and quantum Jensen-Shannon divergence" @default.
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• W2034306513 doi "https://doi.org/10.1103/physreva.79.052311" @default.
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