Abstract

July 5 - 10.50-11.40
H.Hasegawa - On the Dual Geometry of Wigner-Yanase-Dyson Information Quantities

Wigner-Yanase-Dyson conjecture appeared about forty years ago as a subject of mathematical physics concerning the convexity of a matrix-valued information quantity. Lieb gave an affirmative answer to the conjecture in 1973 in the more general context of operator algebras. Another proof of the so-called Wigner-Yanase-Dyson-Lieb concavity was given by Uhlmann in 1977. What interests us about this well-established subject is its information-geometrical significance: it provides us with a typical example of quantum Fisher information, and furthermore this example carries Amari's concept of duality. In the present talk I wish to show that this concept: (a) enables us to sharpen Petz's classification theorem of monotone metrics; (b) characterizes the associated quasi-entropy; (c) introduces naturally (in the framework of matrix analysis) a connection that conforms to Amari's dual connection. [an error occurred while processing this directive]