Leírás
Abstract: In this talk we will review some of the recent developments of information measures in Shannon theory. Information measures came a long way from Shannon through Neumann to the 1960s where most of the central information measures were axiomatized among others by Alfréd Rényi. Recent years have seen another surge in this field and new measures find their purpose year by year.
Among the examples when such measures can be used to characterize transformability questions is the question of reversible channels discussed at this very seminar a few weeks ago. Another example will be given in hypothesis testing and I will show an instance based on our work how one can derive characterizing information measures axiomatically using recent results from semi-ring theory. This argument leads to the renewed need of multivariate quantum divergences and I will shortly discuss some of our results on constructing multivariate divergences from previously known binary divergences and relative entropies. The talk will include an introductory part on Shannon theory and Rényi divergences so that it could be easily followed.