Related papers: New Logical Foundations for Quantum Information Th…
The common-sense view of reality is expressed logically in Boolean subset logic (each element is either definitely in or not in a subset, i.e., either definitely has or does not have a property). But quantum mechanics does not agree with…
Quantum information is defined by applying the concepts of ordinary (Shannon) information theory to a quantum sample space consisting of a single framework or consistent family. A classical analogy for a spin-half particle and other…
The development of the new logic of partitions (= equivalence relations) dual to the usual Boolean logic of subsets, and its quantitative version as the new logical theory of information provide the basic mathematical concepts to describe…
A framework for a quantum mechanical information theory is introduced that is based entirely on density operators, and gives rise to a unified description of classical correlation and quantum entanglement. Unlike in classical (Shannon)…
Geometric quantum mechanics, through its differential-geometric underpinning, provides additional tools of analysis and interpretation that bring quantum mechanics closer to classical mechanics: state spaces in both are equipped with…
Information theory, introduced by Shannon, has been extremely successful and influential as a mathematical theory of communication. Shannon's notion of information does not consider the meaning of the messages being communicated but only…
The Partial Information Decomposition (PID) takes one step beyond Shannon's theory in decomposing the information two variables $A,B$ possess about a third variable $T$ into distinct parts: unique, shared (or redundant) and synergistic…
We analyze the geometry of a joint distribution over a set of discrete random variables. We briefly review Shannon's entropy, conditional entropy, mutual information and conditional mutual information. We review the entropic information…
This paper traces an intellectual journey or \textit{Way} (in the sense of a Tao) that starts with some unfinished work of Gian-Carlo Rota on making a logic of equivalence relations or partitions. Rota understood the category-theoretic…
We review with a tutorial scope the information theory foundations of quantum statistical physics. Only a small proportion of the variables that characterize a system at the microscopic scale can be controlled, for both practical and…
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…
Shannon's theory of information was built on the assumption that the information carriers were classical systems. Its quantum counterpart, quantum Shannon theory, explores the new possibilities arising when the information carriers are…
We reconstruct the explicit formalism of qubit quantum theory from elementary rules on an observer's information acquisition. Our approach is purely operational: we consider an observer O interrogating a system S with binary questions and…
Inspired by a quantum mechanical formalism to model concepts and their disjunctions and conjunctions, we put forward in this paper a specific hypothesis. Namely that within human thought two superposed layers can be distinguished: (i) a…
A survey of various concepts in quantum information is given, with a main emphasis on the distinguishability of quantum states and quantum correlations. Covered topics include generalized and least square measurements, state discrimination,…
I will show how an objective definition of the concept of information and the consideration of recent results about information-processing in the human brain help clarify some fundamental and often counter-intuitive aspects of quantum…
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…
Quantum entanglement of pure states of a bipartite system is defined as the amount of local or marginal ({\em i.e.}referring to the subsystems) entropy. For mixed states this identification vanishes, since the global loss of information…
We show that any quantum information theory based on anticommuting operators must be supplemented by a superselection rule deeply rooted in relativity to establish a reasonable notion of entanglement. While quantum information may be…
Resource identification and quantification is an essential element of both classical and quantum information theory. Entanglement is one of these resources, arising when quantum communication and nonlocal operations are expensive to…