Properties of Classical and Quantum Jensen-Shannon Divergence
| dc.creator | Briët, Jop | |
| dc.creator | Harremoës, Peter | |
| dc.date | 2008-06-27 | |
| dc.date | 2009-04-14 | |
| dc.date.accessioned | 2026-07-07T13:14:16Z | |
| dc.date.available | 2026-07-07T13:14:16Z | |
| dc.description | 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 (JD_alpha for alpha>0), the Jensen divergences of order alpha, which generalize JD as JD_1=JD. Using a result of Schoenberg, we prove that JD_alpha is the square of a metric for alpha lies in the interval (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 alpha (QJD_alpha). We strengthen results by Lamberti et al. by proving that for qubits and pure states, QJD_alpha^1/2 is a metric space which can be isometrically embedded in a real Hilbert space when alpha lies in the interval (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. | |
| dc.description | 13 pages, LaTeX, expanded contents, added references and corrected typos | |
| dc.identifier | https://arxiv.org/abs/0806.4472 | |
| dc.identifier | http://arxiv.org/abs/0806.4472 | |
| dc.identifier | Phys. Rev. A 79, 052311 (2009) | |
| dc.identifier | doi:10.1103/PhysRevA.79.052311 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/230156 | |
| dc.subject | Quantum Physics | |
| dc.title | Properties of Classical and Quantum Jensen-Shannon Divergence | |
| dc.type | text |