Compare Papers
Paper 1
Continuous-time quantum Monte Carlo for fermion-boson lattice models: Improved bosonic estimators and application to the Holstein model
Manuel Weber, Fakher F. Assaad, Martin Hohenadler
- Year
- 2016
- Journal
- Physical Review B
- DOI
- 10.1103/physrevb.94.245138
- arXiv
- -
No abstract.
Open paperPaper 2
Fields of covariances on non-commutative probability spaces in finite dimensions
Florio M. Ciaglia, Fabio Di Cosmo, Laura González-Bravo
- Year
- 2025
- Journal
- arXiv preprint
- DOI
- arXiv:2510.24617
- arXiv
- 2510.24617
We introduce the notion of a field of covariances, a contravariant functor from non-commutative probability spaces to Hilbert spaces, as the natural categorical analogue of statistical covariance. In the case of finite-dimensional non-commutative probability spaces, we obtain a complete classification of such fields. Our results unify classical and quantum information geometry: in the tracial case, we recover (a contravariant version of) Cencov's uniqueness of the Fisher-Rao metric, while in the faithful case, we recover (a contravariant version of) the Morozova-Cencov-Petz classification of quantum monotone metrics. Crucially, our classification extends naturally to non-faithful states that are not pure, thus generalizing Petz and Sudar's radial extension.
Open paper