Majorization relation

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August undefined, 2024

WebBesides uncertainty relations, the concept of majorization is applied to various topics, such as quantum thermodynamics [31] and coherence [32]. The majorization-based UR was … Web3 jan. 2024 · Uncertainty relation is not only of fundamental importance to quantum mechanics, but also crucial to the quantum information technology. Recently, …

Shannon Type Inequalities for Kapur’s Entropy

Web2 jun. 2024 · Quantum majorization is a partial order to rank matrices looking at their eigenvalues. In particular, a matrix is defined riskier than another when the spectrum of the latter belongs to the convex hull spanned by the former. This can be verified by exploiting the so-called majorization relation among positive real vectors (Arnold & Sarabia, 2024). Web22 jul. 2016 · Majorization relations of both: the direct-sum and the tensor-product types are obtained within the developed scheme. The direct-sum majorization relations for … economic history jstor

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Web31 mrt. 2024 · The concept of majorization is explored as a tool to characterize the performance of a quantum Otto engine in the quasistatic regime. For a working … Web1 jul. 2024 · The majorization relation, due to Hardy, Littlewood, and Polya (1929), embodies an elegant notion of “variability” and deﬁnes a partial order among vectors in Euclidean Andreas Kleiner: [email protected] Benny Moldovanu: [email protected] Philipp Strack: [email protected] http://www.teaching.math.rs/vol/tm813.pdf computing is the extension of cloud computing

Majorization relation between the absolute values squared of the ...

Concentration of Multivariate Statistical Tables

Web7 apr. 2024 · Majorization Theory for Unitary Control of Optical Absorption and Emission Cheng Guo 1 ,* and Shanhui Fan 2 , † 1 Department of Applied Physics, Stanford University, Stanford, California 94305, USA In mathematics, majorization is a preorder on vectors of real numbers. Let $${\displaystyle {x}_{(i)}^{},\ i=1,\,\ldots ,\,n}$$ denote the $${\displaystyle i}$$-th largest element of the vector $${\displaystyle \mathbf {x} \in \mathbb {R} ^{n}}$$. Given Meer weergeven (Strong) majorization: $${\displaystyle (1,2,3)\prec (0,3,3)\prec (0,0,6)}$$. For vectors with $${\displaystyle n}$$ components (Weak) … Meer weergeven • Majorization in MathWorld • Majorization in PlanetMath Meer weergeven • OCTAVE/MATLAB code to check majorization Meer weergeven • Muirhead's inequality • Karamata's Inequality • Schur-convex function Meer weergeven 1. ^ Marshall, Albert W. (2011). Inequalities : theory of majorization and its applications. Ingram Olkin, Barry C. Arnold (2nd ed.). New York: Springer Science+Business Media, LLC. Meer weergeven economic history conference 2023Web28 dec. 2024 · Majorization is an order relation for the comparison of two apportionment methods. Some method A is majorized by some other method B when every group of … economic history jobs

"Web31 mrt. 2024 · For a working substance in the form of a single spin of arbitrary magnitude, majorization yields a necessary and sufficient condition for the operation of the Otto engine, provided the canonical distribution of the working medium at the hot reservoir is majorized by its canonical distribution at the cold reservoir. " - Majorization relation

Majorization relation

WebMajorization relation between the absolute values squared of the entries of a matrix and the singular values squared Ask Question Asked 11 years, 11 months ago Modified 11 months ago Viewed 1k times 7 Let A = [Aij] be an n × n square matrix with complex entries, and let σk, k = 1, …, n be its singular values. WebThis relation supplies powerful tools for studying and solving Schrödinger, Dirac, Maxwell, Klein-Gordon and other equations with the aid of complex-analytic methods. The book is dedicated to these recent developments in pseudoanalytic function theory and their applications as well as to multidimensional generalizations.

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Web13 jun. 2024 · Information entropy and its extension, which are important generalizations of entropy, are currently applied to many research domains. In this paper, a novel generalized relative entropy is constructed to avoid some defects of traditional relative entropy. We present the structure of generalized relative entropy after the discussion of defects in … Web5 jun. 2007 · Majorization theory is the underlying mathematical theory on which the framework hinges. It allows the transformation of the originally complicated matrix-valued nonconvex problem into a simple scalar problem.

Web2. Majorization relation for ﬁnite sequences and Karamata’s inequality Let us introduce a majorization relation for ﬁnite sequences of real numbers. Definition 1. Let a =(a1,a2,...,a n)andb =(b1,b2,...,b n) be two (ﬁnite) sequences of real numbers. We say that the sequence a majorizes the sequence b and we write a b or b ≺ a, Web7 apr. 2024 · 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. …

Web11 mrt. 2024 · We derive an entropic uncertainty relation for generalized positive-operator-valued measure (POVM) measurements via a direct-sum majorization relation using … WebAn important problem in quantum information theory is the mathematical characterization of the phenomenon of quantum catalysis: when can the surrounding entanglement be used to perform transformations of a jointly held quantum state under LOCC (local operations and classical communication) ? Mathematically, the question amounts to describe, for a fixed …

Web• Majorization is a preorder defined on real-valued vectors. This gives rise to a natural definition of majorization on the self-adjoint operators through the characterization of its eigenvalues; in quantum information theory, this relation can be defined equivalently by the action of a mixed-unitary channel. One can extend this…

Webmajorization relation, little is known about power majorization. Indeed, it is in general di cult to determine whether one vector is power majorized by another. Our investigation in this paper stems from the following example. 2010 Mathematics Subject Classi cation. 26B10, 26C25. Key words and phrases. power majorization, majorization ... computing iteration definitionWebMaking use ofthe majorization technique we derive explicit lower bounds for the sum of R´enyi entropies describing probability distributions associated with a given pure state … computing iterated integralWeb31 dec. 2024 · Strong Majorization Uncertainty Relations: Theory and Experiment. In spite of enormous theoretical and experimental progresses in quantum uncertainty relations, … computing isogenies between montgomery curvesWeb16 jan. 2024 · The majorization order is a partial order, i.e., not every two vectors are comparable under majorization. When studying majorization among two vectors of … computing jobs scotlandWebIn this paper, we prove the log-majorization relation on the singular values of the product of given positive definite matrices and their (metric and spectral) geometric means. We also establish the weak log-majorization between the spectra of the two-variable Wasserstein mean and spectral geometric mean. computing itWebFrame completions with prescribed norms: local minimizers and applications computing it leaders festivalWeb20 aug. 2024 · We explore the role of majorization theory in quantum phase space. To this purpose, we restrict ourselves to quantum states with positive Wigner functions and … computing it leaders 100