Uniqueness of the Chentsov metric

with Matheus Grasselli. To appear in the proceedings of the conference "Disordered and Complex Systems", King's College London, 10-14 July 2000, published by American Inst. of Physics. Edited by A. C. C. Coolen, L. Hughston, P. Sollich and R. F. Streater

ABSTRACT

We show that on the space of faithful density matrices, the only monotone metrics (those reduced by any completely positive trace-preserving map), for which the exponential and mixture affine connections are mutually dual, are constant multiples of the Bogoliubov-Kubo-Mori (BKM) metric.

Remark. This is a six-page summary of the full version. In the present work, we outline the proof, but also add some details concerning the extension of the metric from the manifold of density matrices to the manifold of the weights, in such a way that the metric continues to be monotone.