Related papers: On the Conditional Smooth Renyi Entropy and its Ap…
Entanglement entropy is an essential metric for characterizing quantum many-body systems, but its numerical evaluation for neural network representations of quantum states has so far been inefficient and demonstrated only for the restricted…
We consider the distributed compression of Soft Random Geometric Graphs (SRGGs) above the connectivity threshold. We establish the Slepian-Wolf rate region for the SRGG in the setting where there are a finite number of encoders compressing…
We consider the problem of distilling uniform random bits from an unknown source with a given $p$-entropy using linear hashing. As our main result, we estimate the expected $p$-divergence from the uniform distribution over the ensemble of…
Entropies must correspond to mean values for them to be measurable. The Shannon entropy corresponds to the weighted arithmetic mean, whereas the Renyi entropy corresponds to the exponential mean. These means refer to code lengths, which are…
Studies on generalization performance of machine learning algorithms under the scope of information theory suggest that compressed representations can guarantee good generalization, inspiring many compression-based regularization methods.…
The fidelity-based smooth min-relative entropy is a distinguishability measure that has appeared in a variety of contexts in prior work on quantum information, including resource theories like thermodynamics and coherence. Here we provide a…
"Bounds on information combining" are entropic inequalities that determine how the information (entropy) of a set of random variables can change when these are combined in certain prescribed ways. Such bounds play an important role in…
We propose that chaotic Glass networks (a class of piecewise-linear Ordinary Differential Equations) are good candidates for the design of true random number generators. A Glass network design has the advantage of involving only standard…
Wyner's soft-covering lemma is the central analysis step for achievability proofs of information theoretic security, resolvability, and channel synthesis. It can also be used for simple achievability proofs in lossy source coding. This work…
We show that the R\'enyi entropies of single particle, extended wave functions for disordered systems contain information about the multifractal spectrum. It is shown for moments of the R\'enyi entropy, $S_{n}$, where $|n|<1$, it is…
We introduce an axiomatic approach to entropies and relative entropies that relies only on minimal information-theoretic axioms, namely monotonicity under mixing and data-processing as well as additivity for product distributions. We find…
By using the Renyi entropy, and following the same scheme that in the Fisher-Renyi entropy product case, a generalized statistical complexity is defined. Several properties of it, including inequalities and lower and upper bounds are…
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…
Conditional graph entropy is known to be the minimal rate for a natural functional compression problem with side information at the receiver. In this paper we show that it can be formulated as an alternating minimization problem, which…
We seek an entropy estimator for discrete distributions with fully empirical accuracy bounds. As stated, this goal is infeasible without some prior assumptions on the distribution. We discover that a certain information moment assumption…
This thesis addresses the interplay between asymptotic hypothesis testing and entropy inequalities in quantum information theory. In the first part of the thesis we focus on hypothesis testing. We consider two main settings; one can either…
This paper investigates the problem of guessing subject to distortion, which was introduced by Arikan and Merhav. While the primary concern of the previous study was asymptotic analysis, our primary concern is non-asymptotic analysis. We…
Maximum Entropy is a powerful concept that entails a sharp separation between relevant and irrelevant variables. It is typically invoked in inference, once an assumption is made on what the relevant variables are, in order to estimate a…
The so-called {\em leakage-chain rule} is a very important tool used in many security proofs. It gives an upper bound on the entropy loss of a random variable $X$ in case the adversary who having already learned some random variables…
The Principle of Maximum Entropy is a rigorous technique for estimating an unknown distribution given partial information while simultaneously minimizing bias. However, an important requirement for applying the principle is that the…