# Maps on quantum states preserving Bregman and Jensen divergences

Időpont:
2017. 03. 22. 16:00
Hely:
H306
Given a differentiable convex function $c$ on a convex subset $S$ of a real normed space, a natural quantity measuring the dissimilarity of the elements of $S$ appears. The Bregman divergence of $x$ and $y$ is the gap between $c(x)$ and $T_{c,y}(x)$, where $T_{c,y}$ denotes the first-order Taylor polynomial of $c$ with basepoint $y$. This notion of divergence is rather general. The Kullback-Leibler divergence, the Umegaki relative entropy, Stein’s loss, the logistic loss, and the squared Euclidean distance are just particular examples of Bregman divergences. We consider a finite-level quantum system and determine the structure of the transformations on its state space preserving the Bregman divergence generated by an arbitrary strictly convex differentiable function. We also derive a similar result concerning Jensen