Related papers: Algebraic Representations of Entropy and Fixed-Par…
The pure quantum entanglement is generalized to the case of mixed compound states on an operator algebra to include the classical and quantum encodings as particular cases. The true quantum entanglements are characterized by quantum…
We consider the central limit theorem for stable laws in the case of the standardized sum of independent and identically distributed random variables with regular probability density function. By showing decay of different entropy…
We formulate a geometric framework in which physical laws emerge from restricted access to microscopic information. Measurement constraints are modeled as a gauge symmetry acting on density operators, inducing a gauge-reduced space of…
Informational entropy is often identified as physical entropy. This is surprising because the two quantities are differently defined and furthermore the former is a subjective quantity while the latter is an objective one. We describe the…
There are three ways to conceptualize entropy: entropy as an extensive thermodynamic quantity of physical systems (Clausius, Boltzmann, Gibbs), entropy as a measure for information production of ergodic sources (Shannon), and entropy as a…
Permutation entropy quantifies the diversity of possible orderings of the values a random or deterministic system can take, as Shannon entropy quantifies the diversity of values. We show that the metric and permutation entropy…
We approach the physical implications of the non-commutative nature of Complementary Observable Algebras (COA) from an information theoretic perspective. In particular, we derive a general \textit{entropic certainty principle} stating that…
Entropy and differential entropy are important quantities in information theory. A tractable extension to singular random variables-which are neither discrete nor continuous-has not been available so far. Here, we present such an extension…
The paper analyzes the entropy of a system composed by non-interacting and indistinguishable particles whose quantum state numbers are modelled as independent and identically distributed classical random variables. The crucial observation…
Problem of classification of all the set of entangled states is considered. Invariance of entangled states relative to transformations from a group of symmetry of qubit space leads to classification of all states of the system through…
We introduce a class of continuous maps f of a compact metric space I admitting inducing schemes and describe the tower constructions associated with them. We then establish a thermodynamical formalism, i.e., describe a class of real-valued…
We derive explicit bounds for the average entropy characterizing measurements of a pure quantum state of size $N$ in $L$ orthogonal bases. Lower bounds lead to novel entropic uncertainty relations, while upper bounds allow us to formulate…
Entropies associated with spatial subsystems in conventional local quantum field theories are typically divergent when the spatial regions have boundaries. However, in certain linear combinations of the entropies for various subsystems,…
We discuss the information entropy for a general open pointer-based simultaneous measurement and show how it is bound from below. This entropic uncertainty bound is a direct consequence of the structure of the entropy and can be obtained…
We advocate the use of a notion of entropy that reflects the relative abundances of the symbols in an alphabet, as well as the similarities between them. This concept was originally introduced in theoretical ecology to study the diversity…
We produce a probabilistic space from logic, both classical and quantum, which is in addition partially ordered in such a way that entropy is monotone. In particular do we establish the following equation: Quantitative Probability = Logic +…
Thermodynamic entropy is not an entirely satisfactory measure of information of a quantum state. This entropy for an unknown pure state is zero, although repeated measurements on copies of such a pure state do communicate information. In…
To study arithmetic structures of natural numbers, we introduce a notion of entropy of arithmetic functions, called anqie entropy. This entropy possesses some crucial properties common to both Shannon's and Kolmogorov's entropies. We show…
Entropy is a fundamental concept in quantum information theory that allows to quantify entanglement and investigate its properties, for example its monogamy over multipartite systems. Here, we derive variational formulas for relative…
A Borel system consists of a measurable automorphism of a standard Borel space. We consider Borel embeddings and isomorphisms between such systems modulo null sets, i.e. sets which have measure zero for every invariant probability measure.…