Related papers: Non-Shannon Information Inequalities in Four Rando…
In 1997, Z.Zhang and R.W.Yeung found the first example of a conditional information inequality in four variables that is not "Shannon-type". This linear inequality for entropies is called conditional (or constraint) since it holds only…
In 1998, Zhang and Yeung found the first unconditional non-Shannon-type information inequality. Recently, Dougherty, Freiling and Zeger gave six new unconditional non-Shannon-type information inequalities. This work generalizes their work…
The entropic region is formed by the collection of the Shannon entropies of all subvectors of finitely many jointly distributed discrete random variables. For four or more variables, the structure of the entropic region is mostly unknown.…
We compare two different techniques for proving non-Shannon-type information inequalities. The first one is the original Zhang-Yeung's method, commonly referred to as the copy/pasting lemma/trick. The copy lemma was used to derive the first…
Upper and lower bounds are obtained for the joint entropy of a collection of random variables in terms of an arbitrary collection of subset joint entropies. These inequalities generalize Shannon's chain rule for entropy as well as…
In the past over two decades, very fruitful results have been obtained in information theory in the study of the Shannon entropy. This study has led to the discovery of a new class of constraints on the Shannon entropy called…
Information inequalities govern the ultimate limitations in information theory and as such play an pivotal role in characterizing what values the entropy of multipartite states can take. Proving an information inequality, however, quickly…
This paper is on developing some computer-assisted proof methods involving non-classical inequalities for Shannon entropy. Two areas of the applications of information inequalities are studied: Secret sharing schemes and hat guessing games.…
Ranks of subspaces of vector spaces satisfy all linear inequalities satisfied by entropies (including the standard Shannon inequalities) and an additional inequality due to Ingleton. It is known that the Shannon and Ingleton inequalities…
Information decompositions quantify how the Shannon information about a given random variable is distributed among several other random variables. Various requirements have been proposed that such a decomposition should satisfy, leading to…
A causal structure is a relationship between observed variables that in general restricts the possible correlations between them. This relationship can be mediated by unobserved systems, modelled by random variables in the classical case or…
An interference alignment perspective is used to identify the simplest instances (minimum possible number of edges in the alignment graph, no more than 2 interfering messages at any destination) of index coding problems where non-Shannon…
We study conditional linear information inequalities, i.e., linear inequalities for Shannon entropy that hold for distributions whose entropies meet some linear constraints. We prove that some conditional information inequalities cannot be…
We exhibit infinitely many new, constrained inequalities for the von Neumann entropy, and show that they are independent of each other and the known inequalities obeyed by the von Neumann entropy (basically strong subadditivity). The new…
The present paper offers, in its first part, a unified approach for the derivation of families of inequalities for set functions which satisfy sub/supermodularity properties. It applies this approach for the derivation of information…
Distributed systems, such as biological and artificial neural networks, process information via complex interactions engaging multiple subsystems, resulting in high-order patterns with distinct properties across scales. Investigating how…
We discuss some inequalities for N nonnegative numbers. We use these inequalities to obtain known inequalities for probability distributions and new entropic and information inequalities for quantum tomograms of qudit states. The…
Using joint Shannon entropy, we propose an inequality for a four-level system, which is satisfied in any non-contextual realist hidden variable model. We show that this entropic inequality is violated by quantum mechanics for a range of…
Information is a valuable asset for agents in socio-economic systems, a significant part of the information being entailed into the very network of connections between agents. The different interlinkages patterns that agents establish may,…
Shannon entropy, a cornerstone of information theory, statistical physics and inference methods, is uniquely identified by the Shannon-Khinchin or Shore-Johnson axioms. Generalizations of Shannon entropy, motivated by the study of…