XXVI International Fall Workshop on Geometry and Physics

Braga, 4-7 September 2017

In this talk, we will explore a little part of the so-called "zoo of monotone quantum metrics". These are all those metrics on the space of (invertible) quantum states behaving nicely under completely-positive, trace-preserving maps. We will start looking at the problem of recovering classical and quantum metrics from two-point functions. In some interesting cases, these two-point functions turn out to be generalized relative entropies. Walking thruogh this road, a way to implement the symmetries of a metric at the level of the relative entropy generating it will be exposed. Then, we will consider a recently introduced family of quantum relative entropies and derive from it a family of quantum metrics satisfying the so-called monotonicity property. It turns out that some well-known quantum metrics like the Bures metric, or the Wigner-Yanase-Dison metric, belong to this (quite big) family. Finally, some thoughts on the tomographic reconstruction of quantum metrics will conclude our trip.

Click here to access the slides.