On the metric character of the quantum Jensen-Shannon divergence
arXiv:0801.1586 · doi:10.1103/PhysRevA.77.052311
Abstract
In a recent paper, the generalization of the Jensen Shannon divergence (JSD) in the context of quantum theory has been studied (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 simulations for mixed states, that its square root verifies the triangle inequality.
8 pages, 1 figures, numerical results substantially improved in Sec. III. To appear in Phys. Rev. A
Cited by in corpus (15)
- Layer aggregation and reducibility of multilayer interconnected networks
- Properties of Classical and Quantum Jensen-Shannon Divergence
- Spectral entropies as information-theoretic tools for complex network comparison
- Quantum coherence of planar spin models with Dzyaloshinsky-Moriya interaction
- Review on Quantum Walk Computing: Theory, Implementation, and Application
- Entropic bounds on information backflow
- Monoparametric family of metrics derived from classical Jensen-Shannon divergence
- On the metric property of quantum Wasserstein divergences
- Lightcone Bounds for Quantum Circuit Mapping via Uncomplexity
- Transmission distance in the space of quantum channels
- Thermal coherence of the Heisenberg model with Dzyaloshinsky-Moriya interactions in an inhomogenous external field
- Information Geometric Security Analysis of Differential Phase Shift Quantum Key Distribution Protocol
- Quantum speed limits based on Jensen-Shannon and Jeffreys divergences for general physical processes
- Perturbative distinguishability of black hole microstates from AdS/CFT correspondence
- Structure Preserving Large Imagery Reconstruction