Intro
Preface
Contents
1 Integration Method Within an Ordered Product of Operators and Continuous-Variable Entangled State Representations
1.1 Integration Method Within an Ordered Product of Operators
1.1.1 Normal Ordering Case
1.1.2 Anti-normal Ordering Case
1.1.3 Weyl Ordering Case
1.2 Two-Particle Entangled State Representation
1.3 Thermal Entangled State Representation
1.3.1 Bosonic Case
1.3.2 Fermionic Case
References
2 Dynamics of Two-Body Hamiltonian Systems
2.1 Energy-Level Distribution and Wave Function of Two-Body Hamiltonian System

2.1.1 Two Moving Charged Particles with Elastic Coupling
2.1.2 Two Moving Charged Particles with Coulomb Coupling
2.2 Path Integral Theory in Entangled State Representation
2.3 Evolution of Atomic Coherent State Governed by the Hamiltonian ...
2.4 Atomic Coherent States as Energy Eigenstates of the Hamiltonian ...
References
3 New Bipartite Entangled States in Two-Mode Fock Space
3.1 Coherent-Entangled States
3.2 Entangled States Describing Parametric Down Conversion
3.3 Parameterized Entangled States Induced by the Common Eigenstates ...

3.4 Parameterized Entangled States as the Common Eigenstates ...
References
4 Solutions of Density Operator Master Equations
4.1 Solutions of Several Boson Master Equations
4.1.1 Diffusion Master Equation Under Linear Resonance Force
4.1.2 Master Equation for Single-Mode Cavity Driven by Oscillating External Field in a Heat Reservoir
4.1.3 Master Equation for Damped Harmonic Oscillator Acted by Linear Resonance Force in a Squeezed Heat Reservoir
4.1.4 Master Equation Describing a Diffusive Anharmonic Oscillator
4.2 Solutions of Several Fermi Quantum Master Equations

4.2.1 Fermi Master Equations for Amplitude Damping and Phase Damping
4.2.2 Master Equation for Fermi Heat Reservoir
4.3 Generation of Displaced Thermal State
References
5 Wigner Distribution Function and Quantum Tomogram via Entangled State Representations
5.1 Wigner Distribution Functions
5.1.1 Wigner Operator Theory
5.1.2 Wigner Distribution Functions for Quantum States
5.2 Quantum-state Tomography
5.2.1 Quantum Tomography
5.2.2 Quantum Tomograms of Quantum States
References
6 Evolution and Decoherence of Quantum States in Open Systems

6.1 Evolution of Quantum States in the Amplitude Damping Channel
6.1.1 Displaced Thermal States
6.1.2 Thermal-State Superpositions
6.1.3 Two-Mode Squeezed Vacuum States
6.2 Evolution of Quantum States in the Laser Process
6.2.1 Squeezed Number States
6.2.2 Squeezed Thermal States
6.2.3 Multi-photon Subtracted Squeezed Vacuum States
6.2.4 Multi-photon Added Two-Mode Squeezed Thermal States
References
7 Generalized Binomial Theorems and Multi-variable Special Polynomials Involving Hermite Polynomials
7.1 Generalized Binomial Theorems Involving Hermite Polynomials