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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.

Aug 14, 2002
Aug 14, 2002

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