Related papers: Tight entropy bound based on p-quasinorms
In this paper, some general properties of Shannon information measures are investigated over sets of probability distributions with restricted marginals. Certain optimization problems associated with these functionals are shown to be…
We present a detailed derivation of some estimators of Shannon entropy for discrete distributions. They hold for finite samples of N points distributed into M "boxes", with N and M -> oo, but N/M < oo. In the high sampling regime (<< 1…
The von Neumann entropy and the subentropy of a mixed quantum state are upper and lower bounds, respectively, on the accessible information of any ensemble consistent with the given mixed state. Here we define and investigate a set of…
We have presented a new axiomatic derivation of Shannon Entropy for a discrete probability distribution on the basis of the postulates of additivity and concavity of the entropy function.We have then modified shannon entropy to take account…
Building on work of Kontsevich, we introduce a definition of the entropy of a finite probability distribution in which the "probabilities" are integers modulo a prime p. The entropy, too, is an integer mod p. Entropy mod p is shown to be…
We consider the entropy of sums of independent discrete random variables, in analogy with Shannon's Entropy Power Inequality, where equality holds for normals. In our case, infinite divisibility suggests that equality should hold for…
We present a near-optimal quantum algorithm, up to logarithmic factors, for estimating the Shannon entropy in the quantum probability oracle model. Our approach combines the singular value separation algorithm with quantum amplitude…
A general upper bound for topological entropy of switched nonlinear systems is constructed, using an asymptotic average of upper limits of the matrix measures of Jacobian matrices of strongly persistent individual modes, weighted by their…
We investigate the uncertainty principle for two successive projective measurements in terms of R\'enyi entropy based on a single quantum system. Our results cover a large family of the entropy (including the Shannon entropy) uncertainty…
Entropic uncertainty relations provide an information-theoretic framework for quantifying the fundamental indeterminacy inherent in quantum mechanics. We propose more stringent quantum-memory-assisted entropic uncertainty relations for…
We consider three von Neumann entropy inequalities: subadditivity; Pinsker's inequality for relative entropy; and the monotonicity of relative entropy. For these we state conditions for equality, and we prove some new error bounds away from…
We prove upper bounds on the rate, called "mixing rate", at which the von Neumann entropy of the expected density operator of a given ensemble of states changes under non-local unitary evolution. For an ensemble consisting of two states,…
We provide finite sample upper and lower bounds on the Binomial tail probability which are a direct application of Sanov's theorem. We then use these to obtain high probability upper and lower bounds on the minimum of i.i.d. Binomial random…
For an indeterminate Hamburger moment problem we consider an infinite family of analytic densities solving the moment problem and we prove that they all have finite (Shannon) entropy. These densities are either all bounded or all unbounded.…
In this paper, we develop the notion of entropy for uniform hypergraphs via tensor theory. We employ the probability distribution of the generalized singular values, calculated from the higher-order singular value decomposition of the…
A novel, non-trivial, probabilistic upper bound on the entropy of an unknown one-dimensional distribution, given the support of the distribution and a sample from that distribution, is presented. No knowledge beyond the support of the…
Quantum entropy is an important measure for describing the uncertainty of a quantum state, more uncertainty in subsystems implies stronger quantum entanglement between subsystems. Our goal in this work is to quantify bipartite entanglement…
The aim of the paper is to study the link between non additivity of some entropies and their boundedness. We propose an axiomatic construction of the entropy relying on the fact that entropy belongs to a group isomorphic to the usual…
We study the $p$-R\'{e}nyi entropy power inequality with a weight factor $t$ on two independent continuous random variables $X$ and $Y$. The extension essentially relies on a modulation on the sharp Young's inequality due to Bobkov and…
We calculate and analyze various entropy measures and their properties for selected probability distributions. The entropies considered include Shannon, R\'enyi, generalized R\'enyi, Tsallis, Sharma-Mittal, and modified Shannon entropy,…