Related papers: Trumping and Power Majorization
The understanding of the meaning of quantization seems to be the main problem in understanding quantum structures. In this paper first the difference between quantized particle vs. radiation fields in the formalism of canonical quantization…
The uncertainty relation lies at the heart of quantum theory and behaves as a non-classical constraint on the indeterminacies of incompatible observables in a system. In the literature, many experiments have been devoted to the test of the…
Random matrix theory has played an important role in various areas of pure mathematics, mathematical physics, and machine learning. From a practical perspective of data science, input data are usually normalized prior to processing. Thus,…
We present a development of norms and discuss their relationship to factorization. In earlier work, the first named author introduced the notion of a normset, which is the image of the norm map. A normset is a monoid with its own…
Recently developed strong-coupling theory open up the possibility of treating quantum-mechanical systems with hard-wall potentials via perturbation theory. To test the power of this theory we study here the exactly solvable quantum…
Entanglement is among the most fundamental-and at the same time puzzling-properties of quantum physics. Its modern description relies on a resource-theoretical approach, which treats entangled systems as a means to enable or accelerate…
A natural link between the notions of majorization and strongly Sperner posets is elucidated. It is then used to obtain a variety of consequences, including new R\'enyi entropy inequalities for sums of independent, integer-valued random…
Free probability theory started in the 1980s has attracted much attention lately in signal processing and communications areas due to its applications in large size random matrices. However, it involves with massive mathematical concepts…
We review the recent developments in the theory of normal, normal self-dual and general complex random matrices. The distribution and correlations of the eigenvalues at large scales are investigated in the large $N$ limit. The 1/N expansion…
We introduce a binary relation on the finite discrete probability distributions which generalizes notions of majorization that have been studied in quantum information theory. Motivated by questions in thermodynamics, our relation describes…
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…
Matching plays a vital role in the rational allocation of resources in many areas, ranging from market operation to people's daily lives. In economics, the term matching theory is coined for pairing two agents in a specific market to reach…
Entanglement detection criteria are developed within the framework of the majorization formulation of uncertainty. The primary results are two theorems asserting linear and nonlinear separability criteria based on majorization relations,…
In this paper, we study majorization for probability distributions and column stochastic matrices. We show that majorizations in general can be reduced to the aforementioned sets. We characterize linear operators that preserve majorization…
Given two pairs of quantum states, a fundamental question in the resource theory of asymmetric distinguishability is to determine whether there exists a quantum channel converting one pair to the other. In this work, we reframe this…
We investigate the relation between degree sequences of trees and the majorization order using the Muirhead theorem. In this way, we prove a theorem that provides a necessary and sufficient condition for delta sequences of trees to be…
The uncertainty principle and entanglement are two fundamental, but yet not well understood, features of quantum theory. The uncertainty relation reflects the capability limit in acquiring the knowledge of different physical properties of a…
Matrix factorization is a simple and effective solution to the recommendation problem. It has been extensively employed in the industry and has attracted much attention from the academia. However, it is unclear what the low-dimensional…
The superposition principle lies at the heart of many non-classical properties of quantum mechanics. Motivated by this, we introduce a rigorous resource theory framework for the quantification of superposition of a finite number of linear…
This paper is about the relation of random matrix theory and the subordination phenomenon in complex analysis. We find that the resolvent of the sum of two random matrices is approximately subordinated to the resolvents of the original…