# 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

#### 56 Citations

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