Abstract

July 4 - 10.50-11.40
M.Grasselli, R.F. Streater - Monotonicity, Duality and Uniqueness of the WYD Metrics

In a previous work, we have found that the Bogoliubov-Kubo-Mori metric is the only monotone metric on finite dimensional quantum systems for which theexponential and mixture connections are mutually dual. It is well established that both the $\pm$-connections and the BKM metric are limiting cases of the more general class of $\alpha$-connections and Wigner-Yanase-Dyson metrics. The present paper extends the uniqueness result mentioned above for this more general class. Namely, for each value of $\alpha \in (-1,1)$, we prove that the only monotone metrics for which the $\pm\alpha$- connections are mutually dual are scalar multiples of the Wigner-Yanase-Dyson metric. [an error occurred while processing this directive]