Related papers: Chain Rules for Smooth Min- and Max-Entropies
We propose a unifying picture where the notion of generalized entropy is related to information theory by means of a group-theoretical approach. The group structure comes from the requirement that an entropy be well defined with respect to…
Entanglement in the ground state of the XY model on the infinite chain can be measured by the von Neumann entropy of a block of neighboring spins. We study a double scaling limit: the size of the block is much larger then 1 but much smaller…
This paper derives bounds for two omnipresent information theoretic measures, the Shannon entropy and its complementary dual, the extropy. Based on a large size data set from a logconcave model, the said bounds are obtained for the entropy…
There are numerous characterizations of Shannon entropy and Tsallis entropy as measures of information obeying certain properties. Using work by Faddeev and Furuichi, we derive a very simple characterization. Instead of focusing on the…
We investigate the concept of entropy in probabilistic theories more general than quantum mechanics, with particular reference to the notion of information causality recently proposed by Pawlowski et. al. (arXiv:0905.2992). We consider two…
Given a probability distribution P, what is the minimum amount of bits needed to store a value x sampled according to P, such that x can later be recovered (except with some small probability)? Or, what is the maximum amount of uniform…
Rare events attract more attention and interests in many scenarios of big data such as anomaly detection and security systems. To characterize the rare events importance from probabilistic perspective, the message importance measure (MIM)…
In this paper, we investigate the asymptotic stability of finite-dimensional stochastic integrable Hamiltonian systems via information entropy. Specifically, we establish the asymptotic vanishing of Shannon entropy difference (with…
Statistical properties of coupled dynamic-stochastic systems are studied within a combination of the maximum information principle and the superstatistical approach. The conditions at which the Shannon entropy functional leads to a…
It is shown that the standard expression for the information entropy, originally due to Shannon, is only valid for a particular set of states. For the general case of statistical mechanics, one needs to include an additional term in the…
Perturbation theory is used to investigate the evolution of the von Neumann entropy of a subsystem of a bipartite quantum system under the action of a unitary matrix, in the limit where that matrix is close to the unit matrix. The physical…
Complementarity relations between various characterizations of a probability distribution are at the core of information theory. In particular, lower and upper bounds for the entropic function are of great importance. In applied topics, we…
We study the notion of approximate entropy within the framework of network theory. Approximate entropy is an uncertainty measure originally proposed in the context of dynamical systems and time series. We firstly define a purely structural…
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…
In quantum information theory, von Neumann entropy plays an important role. The entropies can be obtained analytically only for a few states. In continuous variable system, even evaluating entropy numerically is not an easy task since the…
I consider the effect of a finite sample size on the entropy of a sample of independent events. I propose formula for entropy which satisfies Shannon's axioms, and which reduces to Shannon's entropy when sample size is infinite. I discuss…
The precise one-shot characterisation of operational tasks in classical and quantum information theory relies on different forms of smooth entropic quantities. A particularly important connection is between the hypothesis testing relative…
In Variational Analysis, VU-theory provides a set of tools that is helpful for understanding and exploiting the structure of nonsmooth functions. The theory takes advantage of the fact that at any point, the space can be separated into two…
The concept of Shannon Entropy for probability distributions and associated Maximum Entropy Principle are extended here to the concepts of Relative Divergence of one Grading Function from another and Maximum Relative Divergence Principle…
The von Neumann entropy plays a vital role in quantum information theory. The von Neumann entropy determines, e.g., the capacities of quantum channels. Also, entropies of composite quantum systems are important for future quantum networks,…