Metric character of the quantum Jensen-Shannon divergence
By P. W. Lamberti, A. P. Majtey, A. Borras, M. Casas, A. Plastino. 2008
143 citations recorded by the source corpus.
In a recent paper, the generalization of the Jensen-Shannon divergence in the context of quantum theory has been studied [Majtey et al., Phys. Rev. A 72, 052310 (2005)]. This distance between quantum states has shown to verify several of the properties required for a good distinguishability measure. Here we investigate the metric character of this distance. More precisely we show, formally for pure states and by means of a numerical procedure for mixed states, that its square root verifies the triangle inequality.
Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/b44535caeef06de67a942c22aeacc19a31e85773
How researchers see this paper
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In Artificial Intelligence
- J. Briet
- Isidoros Doxas
- Ingemar Bengtsson
- W. Oliver
- Karol Zyczkowski
- Peter Harremoës
- Fuyuan Xiao
- Simon J. Dennis
In Atomic and Molecular Physics, and Optics
In Statistical and Nonlinear Physics
- J. Briet
- Isidoros Doxas
- Ingemar Bengtsson
- W. Oliver
- Karol Zyczkowski
- Peter Harremoës
- Simon J. Dennis
- Yingzhen Li
Citations in the corpus
- Geometry of Quantum States: Index (2007, background): “2 This was shown in 2003 by Endres and Schindelin [295], and the result is expected to generalise to the quantum case [175, 570].”
- Multi-sensor data fusion based on the belief divergence measure of evidences and the belief entropy (2019, background): “(The JS divergence between two probability distributions) [83,85].”
- Properties of Classical and Quantum Jensen-Shannon Divergence (2008, methodology): “al proved that this is indeed the case for pure-states [6], which lead to the study of the metric formed by the QJSD of purifications of states [8].”
- The dimensionality of discourse (2010, methodology): “Because this measure has been shown tomeet metric criteria (25, 26), it is more appropriate for the correlation dimension analysis than other measures of divergence that do not meet these criteria, such as the Kullback-Leibler divergence.”