Related papers: Inequalities for quantum divergences and the Auden…
When two independent analog signals, X and Y are added together giving Z=X+Y, the entropy of Z, H(Z), is not a simple function of the entropies H(X) and H(Y), but rather depends on the details of X and Y's distributions. Nevertheless, the…
Consider two series $$\sum_{n=1}^\infty\frac{\sin^n\pi\theta n}{n^\alpha},\quad\sum_{n=1}^\infty\frac{\cos^n\pi\theta n}{n^\alpha}.$$ We show that number-theoretical properties of $\theta$ have a strong effect on the convergence when…
In this paper, we explore the concept of pseudo R\'enyi entropy within the context of quantum field theories (QFTs). The transition matrix is constructed by applying operators situated in different regions to the vacuum state. Specifically,…
A framework for deriving R\'enyi entropy-power inequalities (EPIs) is presented that uses linearization and an inequality of Dembo, Cover, and Thomas. Simple arguments are given to recover the previously known R\'enyi EPIs and derive new…
The study of quantum and classical correlations between subsystems is fundamental to understanding many-body physics. In quantum information theory, the quantum mutual information, $I(A;B)$, is a measure of correlation between the…
We investigate the computational hardness of estimating the quantum $\alpha$-R\'enyi entropy ${\rm S}^{\tt R}_{\alpha}(\rho) = \frac{\ln {\rm Tr}(\rho^\alpha)}{1-\alpha}$ and the quantum $q$-Tsallis entropy ${\rm S}^{\tt T}_q(\rho) =…
This paper proposes and studies new quantum version of $f$-divergences, a class of convex functionals of a pair of probability distributions including Kullback-Leibler divergence, Rnyi-type relative entropy and so on. There are several…
The relative entropy is a measure of the distinguishability of two quantum states. A great deal of progress has been made in the study of the relative entropy between an excited state and the vacuum state of a conformal field theory (CFT)…
Clarke and Barron have recently shown that the Jeffreys' invariant prior of Bayesian theory yields the common asymptotic (minimax and maximin) redundancy of universal data compression in a parametric setting. We seek a possible analogue of…
We offer the first operational interpretation of the $\alpha$-z relative entropies, a measure of distinguishability between two quantum states introduced by Jak\v{s}i\'c et al. and Audenaert and Datta. We show that these relative entropies…
Divergences often play important roles for study in information science so that it is indispensable to investigate their fundamental properties. There is also a mathematical significance of such results. In this paper, we introduce some…
Variational techniques have been recently developed to find tighter bounds on the von Neumann entropy in a completely device-independent (DI) setting. This, in turn, has led to significantly improved key rates of DI protocols, in both the…
We show finite-size bounds on the deviation of the optimal type II error from its asymptotic value in the quantum hypothesis testing problem of Stein's lemma with composite null-hypothesis. The proof is based on some simple properties of a…
A well known conjecture of Wigner, Dyson, and Mehta asserts that the (appropriately normalized) $k$-point correlation functions of the eigenvalues of random $n \times n$ Wigner matrices in the bulk of the spectrum converge (in various…
We consider a pair of one-parameter (alpha) families of generalized two-qubit determinantal Hilbert-Schmidt probability distributions, p_{alpha}(|rho^{PT}|) and q_{alpha}(|rho|), where rho is a 4 x 4 density matrix, rho^{PT}, its partial…
The aim of the present paper is to give axiomatic characterization of quantum relative entropy utilizing resource conversion scenario. We consider two sets of axioms: non-asymptotic and asymptotic. In the former setting, we prove that the…
Energetic coherence is indispensable for various operations, including precise measurement of time and acceleration of quantum manipulations. Since energetic coherence is fragile, it is essential to understand the limits in distillation and…
In this letter, we present the unified paradigm on entropy-ruled Einstein diffusion-mobility relation ({\mu}/D ratio) for all dimensional systems (1D, 2D and 3D) of molecules and materials. The different dimension-associated fractional…
We investigate the universal inequalities relating the alpha-Renyi entropies of the marginals of a multi-partite quantum state. This is in analogy to the same question for the Shannon and von Neumann entropy (alpha=1) which are known to…
We prove a tight uniform continuity bound for Arimoto's version of the conditional $\alpha$-R\'enyi entropy, for the range $\alpha \in [0, 1)$. This definition of the conditional R\'enyi entropy is the most natural one among the multiple…