The Bogoliubov inner product in quantum statistics

@article{Petz1993TheBI,
  title={The Bogoliubov inner product in quantum statistics},
  author={D{\'e}nes Petz and G{\'a}bor Fejes T{\'o}th},
  journal={Letters in Mathematical Physics},
  year={1993},
  volume={27},
  pages={205-216}
}
A natural Riemannian geometry is defined on the state space of a finite quantum system by means of the Bogoliubov scalar product which is infinitesimally induced by the (nonsymmetric) relative entropy functional. The basic geometrical quantities, including sectional curvatures, are computed for a two-level quantum system. It is found that the real density matrices form a totally geodesic submanifold and the von Neumann entropy is a monotone function of the scalar curvature. Furthermore, we… Expand
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