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Geometry from divergence functions and complex structures
- Source :
- International Journal of Quantum Information, Volume 18, Issue01, 2020
- Publication Year :
- 2020
-
Abstract
- Motivated by the geometrical structures of quantum mechanics, we introduce an almost-complex structure $J$ on the product $M\times M$ of any parallelizable statistical manifold $M$. Then, we use $J$ to extract a pre-symplectic form and a metric-like tensor on $M\times M$ from a divergence function. These tensors may be pulled back to $M$, and we compute them in the case of an N-dimensional symplex with respect to the Kullback-Leibler relative entropy, and in the case of (a suitable unfolding space of) the manifold of faithful density operators with respect to the von Neumann-Umegaki relative entropy.<br />Comment: 19 pages, comments are welcome!
- Subjects :
- Quantum Physics
Mathematical Physics
Subjects
Details
- Database :
- arXiv
- Journal :
- International Journal of Quantum Information, Volume 18, Issue01, 2020
- Publication Type :
- Report
- Accession number :
- edsarx.2002.02891
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1142/S021974991941020X