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New families of Fisher information and entropy power inequalities for sums of independent random variables are presented. These inequalities relate the information in the sum of $n$ independent random variables to the information contained…
The main topic of this thesis is the proof of two fundamental entropic inequalities for quantum Gaussian channels. Quantum Gaussian channels model the propagation of electromagnetic waves through optical fibers and free space in the quantum…
Gaussian quantum channels are relevant operations in continuous variable systems. In general, given an arbitrary state, the action on it is well-known provided that the quantum channels are completely characterized. In this work, we…
The present paper is devoted to investigation of the entropy reduction and entanglement-assisted classical capacity (information gain) of continuous variable quantum measurements. These quantities are computed explicitly for multimode…
The region of entropic vectors is a convex cone that has been shown to be at the core of many fundamental limits for problems in multiterminal data compression, network coding, and multimedia transmission. This cone has been shown to be…
It is observed that the entropy reduction (the information gain in the initial terminology) of an efficient (ideal or pure) quantum measurement coincides with the generalized quantum mutual information of a q-c channel mapping an a priori…
Entropy comparison inequalities are obtained for the differential entropy $h(X+Y)$ of the sum of two independent random vectors $X,Y$, when one is replaced by a Gaussian. For identically distributed random vectors $X,Y$, these are closely…
In most communication schemes information is transmitted via travelling modes of electromagnetic radiation. These modes are unavoidably subject to environmental noise along any physical transmission medium and the quality of the…
We offer a new point of view on the (Modified) Log-Sobolev inequality and lower bounds on the Ricci-curvature in the setting where the dynamics are obtained as the limit of Markov processes. In this setting, the large deviation rate…
Error entropy is a important nonlinear similarity measure, and it has received increasing attention in many practical applications. The default kernel function of error entropy criterion is Gaussian kernel function, however, which is not…
We prove the conditional Entropy Power Inequality for Gaussian quantum systems. This fundamental inequality determines the minimum quantum conditional von Neumann entropy of the output of the beam-splitter or of the squeezing among all the…
Many important properties of quantum channels are quantified by means of entropic functionals. Characteristics of such a kind are closely related to different representations of a quantum channel. In the Jamio{\l}kowski-Choi representation,…
We prove that the reciprocal of Fisher information of a log-concave probability density $X$ in ${\bf{R}}^n$ is concave in $t$ with respect to the addition of a Gaussian noise $Z_t = N(0, tI_n)$. As a byproduct of this result we show that…
Estimating information-theoretic quantities such as entropy and mutual information is central to many problems in statistics and machine learning, but challenging in high dimensions. This paper presents estimators of entropy via inference…
The expected value of partial perfect information (EVPPI) denotes the value of eliminating uncertainty on a subset of unknown parameters involved in a decision model. The EVPPI can be regarded as a decision-theoretic sensitivity index, and…
We discuss the inadequacy of covariances/correlations and other measures in L2 as relative distance metrics under some conditions. We propose a computationally simple heuristic to transform a map based on standard principal component…
In vector quantization the number of vectors used to construct the codebook is always an undefined problem, there is always a compromise between the number of vectors and the quantity of information lost during the compression. In this text…
Entropy and relative or cross entropy measures are two very fundamental concepts in information theory and are also widely used for statistical inference across disciplines. The related optimization problems, in particular the maximization…
The data processing inequality (DPI) is a fundamental feature of information theory. Informally it states that you cannot increase the information content of a quantum system by acting on it with a local physical operation. When the smooth…
Gaussian mixture distributions are commonly employed to represent general probability distributions. Despite the importance of using Gaussian mixtures for uncertainty estimation, the entropy of a Gaussian mixture cannot be calculated…