Duality versus Dual Flatness in Quantum Information Geometry

revised version: August 2002
Nihat Ay and Wilderich Tuschmann
(Please use for correspondence this email).

Submission date: 14. Aug. 2002
Pages: 13
published in: Journal of mathematical physics, 44 (2003) 4, p. 1512-1518 
DOI number (of the published article): http://link.aip.org/link/?JMAPAQ/44/1512/1
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Abstract:
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.