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

Communications in Theoretical Physics

Quantum Mechanical Image of Matrices' LDU Decomposition

Fan Hong‐Yi, Yuan Shao-Jie

Published Jun 1, 2010• 0 citations
Publisher

Abstract

For classical transformation ( q 1 , q 2 ) → ( A q 1 + B q 2 , C q 1 + D q 2 ), where AD – CB ≠ 1, we find its quantum mechanical image by using LDU decomposition of the matrix . The explicit operators , , and Û are derived and their physical meaning is revealed, this also provides a new way for disentangling some exponential operators.

DOI
10.1088/0253-6102/53/6/05

Related papers

Quantum mechanical exponential operators' disentangling by virtue of matrices' L\mathfrak{D}U decomposition

Hong-Yi Fan, Yuan Shao-Jie

By using decomposition of the 3 ? 3 real matrix and Dirac's coordinate representation we can derive disentangling of some exponential operators, which is useful for analyzing both squeezing and entangling mechanisms. This method may be generalized to the n ? n real matrix case.

Journal of Physics A Mathematical and Theoretical•Jun 19, 2008•1 citation

Coherent State Representation for a Kind of Operator Disentangling Formulae

Fan Hong‐Yi, Zou Hui, Hui Wang

We derive a kind of operator disentangling formulae and their coherent state representation by virtue of the correspondence between symplectic transformations and their quantum mechanical images. The application of the formulae in calculating Feynman transformation matrix elements is discussed.

Communications in Theoretical Physics•Oct 30, 2000•0 citations

Analysis of the Structure of Transformation Function in Quantum Mechanics

Smio Tani

A new device in operator calculus is introduced to treat expressions which contain non-commutable factors. By means of this technique the defining equation for the generator of transformation function of exponential type is derived. It is shown that this equation contains exclusively commutators of relevant quantities. Then, making use of this peculiarity to the exponential formula, a method is proposed for analyzing the structure of transformation function out of a given Hamiltonian of the system, and this is explained by some examples. This method consists of following procedures: First, decomposition of given Hamiltonian into parts of different character and abstraction of elementary matrices from it. Second, formation of commutators between these matrices and extension, if necessary, of the set of matrices enumerated at the beginning to include new ones which appear through operation of commutation. The matrix ring thus obtained constitutes the frame work of the transformation function. Through the course of this analysis one can find the ground why problems which are already solved exactly can be treated easily, and also can obtain some instructions how one should proceed in the solution of a given problem.

Progress of Theoretical Physics•Feb 1, 1954•8 citations

Linear transformations

Helmut Bez, Tony Croft

This chapter discusses the linear transformations and shows how they can be represented by matrices. It introduces the terms ‘kernel’ and ‘image’ and a result known as the ‘dimension theorem’. Linear transformations are functions which have additional properties which mean that the vector space operations of vector addition and scalar multiplication are preserved. The chapter introduces general linear transformations and shows how they can be represented by matrices. It introduces the terms ‘kernel’ and ‘image’ and a result known as the ‘dimension theorem’. Linear operators are essential to the study of quantum computation because they represent physical observables and determine the time evolution of a quantum system.

Chapman & Hall/CRC eBooks•Jan 6, 2023•0 citations

The quantum way to diagonalize hermitean matrices

Stefan Weigert

Abstract An entirely quantum mechanical approach to diagonalize hermitean matrices has been presented recently. The method is based on the measurement of quantum mechanical observables which provides the computational resource. In brief, quantum mechanics is able to directly address and output eigenvalues of hermitean matrices. Here, the example of (2×2) matrices is considered in detail. This simple case allows one to illustrate the conceptual features of the general method which is applicable to (N×N) hermitean matrices.

arXiv:quant-ph/0305140•Fortschritte der Physik•Feb 26, 2003•2 citations

Quantum Mechanical Image of Matrices＇ LDU Decomposition

范洪义, 袁少杰

为古典转变(q1， q2 )(Aq1 + Bq2， Cq1 + Dq2 ) 广告 CB 1，我们由使用矩阵的 LDU 分解发现它的量机械图象。明确的操作员，，并且？被导出，他们的物理意思被揭示，这也为解开一些指数的操作员提供一个新方法。

理论物理通讯：英文版•Jan 1, 2010•0 citations
For classical transformation ( q 1 , q 2 ) → ( A q 1 + B q 2 , C q 1 + D q 2 ), where AD – CB ≠ 1, we find its quantum mechanical image by using LDU decomposition of the matrix . The explicit operators , , and Û are derived and their physical meaning is revealed, this also provides a new way for disentangling some exponential operators.
A new device in operator calculus is introduced to treat expressions which contain non-commutable factors. By means of this technique the defining equation for the generator of transformation function of exponential type is derived. It is shown that this equation contains exclusively commutators of relevant quantities. Then, making use of this peculiarity to the exponential formula, a method is proposed for analyzing the structure of transformation function out of a given Hamiltonian of the system, and this is explained by some examples. This method consists of following procedures: First, decomposition of given Hamiltonian into parts of different character and abstraction of elementary matrices from it. Second, formation of commutators between these matrices and extension, if necessary, of the set of matrices enumerated at the beginning to include new ones which appear through operation of commutation. The matrix ring thus obtained constitutes the frame work of the transformation function. Through the course of this analysis one can find the ground why problems which are already solved exactly can be treated easily, and also can obtain some instructions how one should proceed in the solution of a given problem.
This chapter discusses the linear transformations and shows how they can be represented by matrices. It introduces the terms ‘kernel’ and ‘image’ and a result known as the ‘dimension theorem’. Linear transformations are functions which have additional properties which mean that the vector space operations of vector addition and scalar multiplication are preserved. The chapter introduces general linear transformations and shows how they can be represented by matrices. It introduces the terms ‘kernel’ and ‘image’ and a result known as the ‘dimension theorem’. Linear operators are essential to the study of quantum computation because they represent physical observables and determine the time evolution of a quantum system.
Abstract An entirely quantum mechanical approach to diagonalize hermitean matrices has been presented recently. The method is based on the measurement of quantum mechanical observables which provides the computational resource. In brief, quantum mechanics is able to directly address and output eigenvalues of hermitean matrices. Here, the example of (2×2) matrices is considered in detail. This simple case allows one to illustrate the conceptual features of the general method which is applicable to (N×N) hermitean matrices.