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Maps on positive definite operators preserving the quantum $\chi_\alpha^2$-divergence
- Source :
- Lett. Math. Phys. 107(12) (2017), 2267-2290
- Publication Year :
- 2017
-
Abstract
- We describe the structure of all bijective maps on the cone of positive definite operators acting on a finite and at least two-dimensional complex Hilbert space which preserve the quantum $\chi_\alpha^2$-divergence for some $\alpha \in [0,1]$. We prove that any such transformation is necessarily implemented by either a unitary or an antiunitary operator. Similar results concerning maps on the cone of positive semidefinite operators as well as on the set of all density operators are also derived.
Details
- Database :
- arXiv
- Journal :
- Lett. Math. Phys. 107(12) (2017), 2267-2290
- Publication Type :
- Report
- Accession number :
- edsarx.1701.02523
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1007/s11005-017-0989-0