Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1009.2210

A Survey of Dynamical Matrices Theory

Lin Zhang, Junde Wu

Published Sep 12, 2010• 1 citation
arXivHTMLPDF

Abstract

In this note, we survey some elementary theorems and proofs concerning dynamical matrices theory. Some mathematical concepts and results involved in quantum information theory are reviewed. A little new result on the matrix representation of quantum operation are obtained. And best separable approximation for quantum operations is presented.

DOI
10.48550/arxiv.1009.2210

Related papers

Dynamic Matrices and Quantum Qubit Arithmetic

Jincheng Zhang

This paper investigates the application of dynamic matrices and quantum qubit arithmetic to revolutionize matrix operations. The core focus is the development of a novel non-linear mapping for dynamic matrices, leveraging the power of quantum qubit arithmetic to achieve a form of quantum computation within the context of matrix operations. Mathematical rigor is employed throughout, providing a detailed analysis of the proposed mechanism and its implications for computational efficiency and potential algorithmic advancements. The paper concludes with a validation of the core concepts through rigorous mathematical proofs.

•Aug 31, 2026•0 citations

Applications of Matrix in Quantum Computation and Quantum Information

Wang Xiao-hong

We introduce some important matrices and their applications in quantum computation and quantum information,including density matrix,unitary matrix,etc.

College Mathematics•Jan 1, 2007•0 citations

Elementary proofs of two theorems involving arguments of eigenvalues of a product of two unitary matrices

H. F. Chau, Yan Ting Lam

We give elementary proofs of two theorems concerning bounds on the maximum argument of the eigenvalues of a product of two unitary matrices--one by Childs et al. [J. Mod. Phys. 47 , 155 (2000)] and the other one by Chau [Quant. Inf. Comp. 11 , 721 (2011)]. Our proofs have the advantages that the necessary and sufficient conditions for equalities are apparent and that they can be readily generalized to the case of infinite-dimensional unitary operators.

arXiv:1006.3978•Journal of Inequalities and Applications•Jul 18, 2011•4 citations

Matrix analysis and quantum information

Fumio Hiai

This survey article treats, by highlighting the role of matrix analysis, some topics from quantum information, mostly related to quantum (relative) entropies and divergences.

Sugaku Expositions•Mar 17, 2017•3 citations

Unknown quantum states: The quantum de Finetti representation

Carlton M. Caves, Christopher A. Fuchs, Rüdiger Schack

We present an elementary proof of the quantum de Finetti representation theorem, a quantum analog of de Finetti’s classical theorem on exchangeable probability assignments. This contrasts with the original proof of Hudson and Moody [Z. Wahrschein. verw. Geb. 33, 343 (1976)], which relies on advanced mathematics and does not share the same potential for generalization. The classical de Finetti theorem provides an operational definition of the concept of an unknown probability in Bayesian probability theory, where probabilities are taken to be degrees of belief instead of objective states of nature. The quantum de Finetti theorem, in a closely analogous fashion, deals with exchangeable density-operator assignments and provides an operational definition of the concept of an “unknown quantum state” in quantum-state tomography. This result is especially important for information-based interpretations of quantum mechanics, where quantum states, like probabilities, are taken to be states of knowledge rather than states of nature. We further demonstrate that the theorem fails for real Hilbert spaces and discuss the significance of this point.

arXiv:quant-ph/0104088•Journal of Mathematical Physics•Sep 1, 2002•445 citations

Quantum Permutation Matrices

Moritz Weber

Abstract Quantum permutations arise in many aspects of modern “quantum mathematics”. However, the aim of this article is to detach these objects from their context and to give a friendly introduction purely within operator theory. We define quantum permutation matrices as matrices whose entries are operators on Hilbert spaces; they obey certain assumptions generalizing classical permutation matrices. We give a number of examples and we list many open problems. We then put them back in their original context and give an overview of their use in several branches of mathematics, such as quantum groups, quantum information theory, graph theory and free probability theory.

Complex Analysis and Operator Theory•Mar 15, 2023•9 citations
In this note, we survey some elementary theorems and proofs concerning dynamical matrices theory. Some mathematical concepts and results involved in quantum information theory are reviewed. A little new result on the matrix representation of quantum operation are obtained. And best separable approximation for quantum operations is presented.
This paper investigates the application of dynamic matrices and quantum qubit arithmetic to revolutionize matrix operations. The core focus is the development of a novel non-linear mapping for dynamic matrices, leveraging the power of quantum qubit arithmetic to achieve a form of quantum computation within the context of matrix operations. Mathematical rigor is employed throughout, providing a detailed analysis of the proposed mechanism and its implications for computational efficiency and potential algorithmic advancements. The paper concludes with a validation of the core concepts through rigorous mathematical proofs.
We present an elementary proof of the quantum de Finetti representation theorem, a quantum analog of de Finetti’s classical theorem on exchangeable probability assignments. This contrasts with the original proof of Hudson and Moody [Z. Wahrschein. verw. Geb. 33, 343 (1976)], which relies on advanced mathematics and does not share the same potential for generalization. The classical de Finetti theorem provides an operational definition of the concept of an unknown probability in Bayesian probability theory, where probabilities are taken to be degrees of belief instead of objective states of nature. The quantum de Finetti theorem, in a closely analogous fashion, deals with exchangeable density-operator assignments and provides an operational definition of the concept of an “unknown quantum state” in quantum-state tomography. This result is especially important for information-based interpretations of quantum mechanics, where quantum states, like probabilities, are taken to be states of knowledge rather than states of nature. We further demonstrate that the theorem fails for real Hilbert spaces and discuss the significance of this point.
Abstract Quantum permutations arise in many aspects of modern “quantum mathematics”. However, the aim of this article is to detach these objects from their context and to give a friendly introduction purely within operator theory. We define quantum permutation matrices as matrices whose entries are operators on Hilbert spaces; they obey certain assumptions generalizing classical permutation matrices. We give a number of examples and we list many open problems. We then put them back in their original context and give an overview of their use in several branches of mathematics, such as quantum groups, quantum information theory, graph theory and free probability theory.