MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Duality versus Dual Flatness in Quantum Information Geometry

Nihat Ay and Wilderich Tuschmann


We show that the set of density operators of a given rank admits dually flat connections for which one connection is complete if and only if this rank is maximal. We prove moreover that there is never a dually flat structure on the set of pure states. Thus any general theory of quantum information geometry that involves duality concepts must inevitably be based on dual structures which are non-flat.


Related publications

2003 Repository Open Access
Nihat Ay and Wilderich Tuschmann

Duality versus dual flatness in quantum information geometry

In: Journal of mathematical physics, 44 (2003) 4, pp. 1512-1518