Estimating quasi-long-range order via Rényi entropies

Joint Range of Rényi Entropies

The exact range of the joined values of several Rényi entropies is determined. The method is based on topology with special emphasis on the orientation of the objects studied.

Swiveled Rényi entropies

This paper introduces “swiveled Rényi entropies” as an alternative to the Rényi entropic quantities put forward in [Berta et al., Physical Review A 91, 022333 (2015)]. What distinguishes the swiveled Rényi entropies from the prior proposal of Berta et al. is that there is an extra degree of freedom: an optimization over unitary rotations with respect to particular fixed bases (swivels). A conse...

Strong converse theorems using Rényi entropies

Rényi entropies and nonlinear diffusion equations

Since their introduction in the early sixties [20], the Rényi entropies have been used in many contexts, ranging from information theory to astrophysics, turbulence phenomena and others. In this note, we enlighten the main connections between Rényi entropies and nonlinear diffusion equations. In particular, it is shown that these relationships allow to prove various functional inequalities in s...

On the Rényi divergence and the joint range of relative entropies

This paper starts with a study of the minimum of the Rényi divergence subject to a fixed (or minimal) value of the total variation distance. Relying on the solution of this minimization problem, we determine the exact region of the points ( D(Q||P1), D(Q||P2) ) where P1 and P2 are any probability distributions whose total variation distance is not below a fixed value, and the probability distri...