Related papers: R\'enyi entropies and nonlinear diffusion equation…
We study the R\'enyi entropies in the spin-$1/2$ anisotropic Heisenberg chain after a quantum quench starting from the N\'eel state. The quench action method allows us to obtain the stationary R\'enyi entropies for arbitrary values of the…
Uncertainty relations have become the trademark of quantum theory since they were formulated by Bohr and Heisenberg. This review covers various generalizations and extensions of the uncertainty relations in quantum theory that involve the…
Estimation of Shannon and R\'enyi entropies of unknown discrete distributions is a fundamental problem in statistical property testing and an active research topic in both theoretical computer science and information theory. Tight bounds on…
In this work, we prove uniform continuity bounds for entropic quantities related to the sandwiched R\'enyi divergences such as the sandwiched R\'enyi conditional entropy. We follow three different approaches: The first one is the "almost…
In this paper, we establish a general relation which directly links the dissipated work done on a system driven arbitrarily far from equilibrium, a fundamental quantity in thermodynamics, and the R\'{e}nyi divergences, a fundamental concept…
Thanks to Pfaffian techniques, we study the R\'enyi entanglement entropies and the entanglement spectrum of large subsystems for two-dimensional Rokhsar-Kivelson wave functions constructed from a dimer model on the triangular lattice. By…
Thermodynamics and information theory have been intimately related since the times of Maxwell and Boltzmann. Recently it was shown that the dissipated work in an arbitrary non-equilibrium process is related to the R\'{e}nyi divergences…
Uncertainty relations for a pair of arbitrary measurements and for a single measurement are posed in the form of inequalities using the Renyi entropies. The formulation deals with discrete observables. Both the relations with…
We explore a large class of correlation measures called the $\alpha-z$ R\'enyi mutual informations (RMIs). Unlike the commonly used notion of RMI involving linear combinations of R\'enyi entropies, the $\alpha-z$ RMIs are positive…
Entropy is a measure of self-information which is used to quantify losses. Entropy was developed in thermodynamics, but is also used to compare probabilities based on their deviating information content. Corresponding model uncertainty is…
We compute the R\'enyi entropies of the massless Dirac field on the Euclidean torus (the Lorentzian cylinder at non-zero temperature) for arbitrary spatial regions. We do it by the resolvent method, i.e., we express the entropies in terms…
Recently, there has been a surge of interest in using R\'enyi entropies as quantifiers of correlations in many-body quantum systems. However, it is well known that in general these entropies do not satisfy the strong subadditivity…
We compute R\'enyi entropies for the statistics of a noisy simultaneous observation of two complementary observables in two-dimensional quantum systems. The relative amount of uncertainty between two states depends on the uncertainty…
We associate to the p-th R\'enyi entropy a definition of entropy power, which is the natural extension of Shannon's entropy power and exhibits a nice behaviour along solutions to the p-nonlinear heat equation in $R^n$. We show that the…
A large class of strongly correlated quantum systems can be described in certain large-N limits by quadratic in field actions along with self-consistency equations that determine the two-point functions. We use the replica approach and the…
We extend from the hyperfinite setting to general von Neumann algebras Mosonyi and Ogawa's (2015) and Mosonyi and Hiai's (2023) results showing the operational interpretation of sandwiched relative R\'enyi entropy in the strong converse of…
We prove the existence and uniqueness of entropy solutions for nonlinear diffusion equations with nonlinear conservative gradient noise. As particular applications our results include stochastic porous media equations, as well as the…
We provide the sandwiched R\'enyi divergence of order $\alpha\in(\frac{1}{2},1)$, as well as its induced quantum information quantities, with an operational interpretation in the characterization of the exact strong converse exponents of…
Entropy is one of the central quantities in thermodynamics, whose flow between two systems determines the statistics of energy transfers. In quantum systems entropy is non-linear in density matrix whose time evolution is cumbersome. Using…
It is shown that the structure of thermodynamics is "form invariant", when it is derived using maximum entropy principle for various choices of entropy and even beyond equilibrium. By the form invariance of thermodynamics, it is meant that…