Related papers: Towards a Semantic Information Theory (Introducing…
This thesis establishes a number of connections between foundational issues in quantum theory, and some quantum information applications. It starts with a review of quantum contextuality and non-locality, multipartite entanglement…
This note will introduce some notation and definitions for information theoretic quantities in the context of quantum systems, such as (conditional) entropy and (conditional) mutual information. We will employ the natural C*-algebra…
A method of representing probabilistic aspects of quantum systems is introduced by means of a density function on the space of pure quantum states. In particular, a maximum entropy argument allows us to obtain a natural density function…
Even today, the concept of entropy is perceived by many as quite obscure. The main difficulty is analyzed as being fundamentally due to the subjectivity and anthropocentrism of the concept that prevent us to have a sufficient distance to…
Fermionic (atomic nuclei) and bosonic (correlated atoms in a trap) systems are studied from an information-theoretic point of view. Shannon and Onicescu information measures are calculated for the above systems comparing correlated and…
We characterize information as risk reduction between knowledge states represented by partitions of the underlying probability space. Entropy corresponds to risk reduction from no (or partial) knowledge to full knowledge about a random…
Quantum information-theoretic approach has been identified as a way to understand the foundations of quantum mechanics as early as 1950 due to Shannon. However there hasn't been enough advancement or rigorous development of the subject. In…
Over the past decade quantum information theory has developed into a vigorous field of research despite the fact that quantum information, as a precise concept, is undefined. Indeed the very idea of viewing quantum states as carriers of…
In this thesis I present a short review of ideas in quantum information theory. The first chapter contains introductory material, sketching the central ideas of probability and information theory. Quantum mechanics is presented at the level…
While semantic communication (SemCom) has recently demonstrated great potential to enhance transmission efficiency and reliability by leveraging machine learning (ML) and knowledge base (KB), there is a lack of mathematical modeling to…
As our world grows increasingly connected and new technologies arise, global demands for data traffic continue to rise exponentially. Limited by the fundamental results of information theory, to meet these demands we are forced to either…
Information theory gives rise to a novel method for causal skeleton discovery by expressing associations between variables as tensors. This tensor-based approach reduces the dimensionality of the data needed to test for conditional…
In this work, we derive information-theoretic properties for a modified Tsallis entropy, hereinafter referred to as q-entropy. We introduce the notions of joint q-entropy, conditional q-entropy, relative q-entropy, conditional mutual…
This paper proposes a reconciliation of two different theories of information. The first, originally proposed in a lesser-known work by Claude Shannon, describes how the information content of channels can be described qualitatively, but…
The information-theoretic representation of quantum systems, which complements the familiar energy description of the density-functional and wave-function-based theories, is here discussed. According to it, the internal disorder of the…
It is von Neumann who opened the window for today's Information epoch. He defined quantum entropy including Shannon's information more than 20 years ahead of Shannon, and he introduced a concept what computation means mathematically. In…
The Shannon-Weaver model of linear information transmission is extended with two loops potentially generating redundancies: (i) meaning is provided locally to the information from the perspective of hindsight, and (ii) meanings can be…
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…
Information theory plays a central role in establishing fundamental limits on what any learning or estimation algorithm can -- and cannot -- achieve, regardless of computational power. In this chapter, we provide an introduction to these…
For noncomposite systems in classical and quantum domains, we obtain new inequalities such as the subadditivity and strong subadditivity conditions for Shannon entropies and information determined by the probability distributions and for…