Related papers: The Neutrosophic Entropy and its Five Components
The paper examines the geometrical properties of a six-dimensional Kaluza-Klein type model. They may have an impact on the model of the structure of a neutron and its excited states in the realm of one particle physics. The statistical…
Quantum uncertainty relations are typically analyzed for a pair of incompatible observables, however, the concept per se naturally extends to situations of more than two observables. In this work, we obtain tripartite quantum…
Combinatorics studies how discrete objects can be counted, arranged, and combined under specified rules. Motivated by uncertainty in real-world data and decisions, modern set-theoretic formalisms such as fuzzy sets, neutrosophic sets, rough…
The holographic representation of the entanglement entropy of four dimensional conformal field theories is studied. By generalizing the replica trick the anomalous terms in the entanglement entropy are evaluated. The same terms in the…
We develop an exact analytical formulation of neutrino oscillations in matter within the framework of the Standard Neutrino Model assuming 3 Dirac Neutrinos. Our Hamiltonian formulation, which includes CP violation, leads to expressions for…
This paper is an introduction to the von Neumann entropy in a historic approach. Von Neumann's gedanken experiment is repeated, which led him to the formula of thermodynamic entropy of a statistical operator. In the analysis of his ideas we…
A general method for proving continuity of the von Neumann entropy on subsets of positive trace-class operators is considered. This makes it possible to re-derive the known conditions for continuity of the entropy in more general forms and…
In this paper, we mainly establish the uncertainty principle (UP) for a function and its quaternion Fractional Fourier transform (QFrFT), as well as the UP for two QFrFTs. Using the polar representation of quaternion-valued signals, we give…
We show the equivalences of several notions of entropy, like a version of the topological entropy of the geodesic flow and the Minkowski dimension of the boundary, in metric spaces with convex geodesic bicombings satisfying a uniform…
We develop a general method for computing logarithmic and log-gamma expectations of distributions. As a result, we derive series expansions and integral representations of the entropy for several fundamental distributions, including the…
We study the behavior of bipartite entanglement at fixed von Neumann entropy. We look at the distribution of the entanglement spectrum, that is the eigenvalues of the reduced density matrix of a quantum system in a pure state. We report the…
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…
This manuscript introduces a computationally efficient method to calculate the nonlinearity of a quantum feature map, as well as a method for determining whether a quantum feature map will have a high concentration of quantum states. The…
We investigate four different types of representations of deformed canonical variables leading to generalized versions of Heisenberg's uncertainty relations resulting from noncommutative spacetime structures. We demonstrate explicitly how…
Given a categorical dynamical system, i.e. a triangulated category together with an endofunctor, one can try to understand the complexity of the system by computing the entropy of the endofunctor. Computing the entropy of the composition of…
An essential quantity in quantum information theory is the von Neumann entropy which depends entirely on the quantum density operator. Once known, the density operator reveals the statistics of observables in a quantum process, and the…
Entropic uncertainty relations, based on sums of entropies of probability distributions arising from different measurements on a given pure state, can be seen as a generalization of the Heisenberg uncertainty relation that is in many cases…
We give a closed-form solution of von Neumann entropy as a function of geometric phase modulated by visibility and average distinguishability in Hilbert spaces of two and three dimensions. We show that the same type of dependence also…
This work presents a systematic investigation into the latent knowledge encoded within Network Foundation Models (NFMs) that focuses on hidden representations analysis rather than pure downstream task performance. Different from existing…
The uncertainty principle can be expressed in entropic terms, also taking into account the role of entanglement in reducing uncertainty. The information exclusion principle bounds instead the correlations that can exist between the outcomes…