Related papers: A Complementary Inequality to the Information Mono…
A nonadditive generalization of Klimontovich's S-theorem [G. B. Bagci, Int.J. Mod. Phys. B 22, 3381 (2008)] has recently been obtained by employing Tsallis entropy. This general version allows one to study physical systems whose stationary…
In this paper we investigate the inequality $S_q(\rho_{123})+S_q(\rho_2)\leq S_q(\rho_{12})+S_q(\rho_{23}) \, (*)$ where $\rho_{123}$ is a state on a finite dimensional Hilbert space $\mathcal{H}_1\otimes \mathcal{H}_2\otimes…
We revisit the monotonicity of relative entropy under the action of quantum channels, a foundational result in quantum information theory. Among the several available proofs, we focus on those by Petz and Uhlmann, which we reformulate…
Minimization problems with respect to a one-parameter family of generalized relative entropies are studied. These relative entropies, which we term relative $\alpha$-entropies (denoted $\mathscr{I}_{\alpha}$), arise as redundancies under…
We discuss some inequalities for N nonnegative numbers. We use these inequalities to obtain known inequalities for probability distributions and new entropic and information inequalities for quantum tomograms of qudit states. The…
Some of the important inequalities associated with quantum entropy are immediate algebraic consequences of the Hansen-Pedersen-Jensen inequality. A general argument is given using matrix perspectives of operator convex functions. A matrix…
We revisit and improve joint concavity/convexity and monotonicity properties of quasi-entropies due to Petz in a new fashion. Then we characterize equality cases in the monotonicity inequalities (the data-processing inequalities) of…
Upper and lower bounds are obtained for the joint entropy of a collection of random variables in terms of an arbitrary collection of subset joint entropies. These inequalities generalize Shannon's chain rule for entropy as well as…
Algorithmic entropy and Shannon entropy are two conceptually different information measures, as the former is based on size of programs and the later in probability distributions. However, it is known that, for any recursive probability…
Gibbs-Boltzmann entropy leads to systems that have a strong dependence on initial conditions. In reality, most materials behave quite independently of initial conditions. Nonextensive entropy or Tsallis entropy leads to nonextensive…
We develop an information-theoretic perspective on some questions in convex geometry, providing for instance a new equipartition property for log-concave probability measures, some Gaussian comparison results for log-concave measures, an…
Uncertainty relations emerging from the Tsallis entropy are derived and discussed. In particular we found a positively defined function that saturates the so called entropic inequalities for entropies characterizing the physical states…
Entropic uncertainty relations are interesting in their own rights as well as for a lot of applications. Keeping this in mind, we try to make the corresponding inequalities as tight as possible. The use of parametrized entropies also allows…
Some new reverses of the Cauchy-Schwarz inequality in inner product spaces are presented in this paper.The results obtained here complement the recent work of the references.
We discuss conditional Renyi and Tsallis entropies for bipartite quantum systems of finite dimension. We investigate the relation between the positivity of conditional entropies and entanglement properties. It is in particular shown that…
A new method is proposed for analyzing complexity and studying the information in random geometric networks using Tsallis entropy tool. Tsallis entropy of the ensemble of random geometric networks is calculated based on the components of…
The connection between inequalities in additive combinatorics and analogous versions in terms of the entropy of random variables has been extensively explored over the past few years. This paper extends a device introduced by Ruzsa in his…
We revisit entropic formulations of the uncertainty principle for an arbitrary pair of positive operator-valued measures (POVM) $A$ and $B$, acting on finite dimensional Hilbert space. Salicr\'u generalized $(h,\phi)$-entropies, including…
The paper describes various approaches to the invertibility of Toeplitz plus Hankel operators in Hardy and $l^p$-spaces, integral and difference Wiener-Hopf plus Hankel operators and generalized Toeplitz plus Hankel operators. Special…
We numerically investigate entropic Bell inequalities for a pair of entangled qutrits using information-theoretic distances. We show that for this class of inequalities Tsallis entropy is more suitable than Shannon as it reveals…