Wigner function of optical cumulant operator and its dissipation in thermo-entangled state representation

To conveniently calculate the Wigner function of the optical cumulant operator and its dissipation evolution in a thermal environment, in this paper, the thermo-entangled state representation is introduced to derive the general evolution formula of the Wigner function, and its relation to Weyl correspondence is also discussed. The method of integration within the ordered product of operators is essential to our discussion.

State Representation Methodology （SRM） for Bridge Condition Assessment in SHM

This paper introduces a new concept of ＂State Representation Methodology （SRM）＂ which is a kind of bridge condition assessment method for structural health monitoring system （SHM）. There are many methods for system identification from the simplicity comparison of damage index to the complicated statistical pattern recognition algorithms in SHM. In these methods, modal analysis and parameters identification or many defined indices are common-used for extracting the dynamic or static characteristics of a system. However, there is a common problem： due to the complexity of a large size system with high-order nonlinear characteristics and severe environment interference, it is impossible to extract and quantify exactly these modal parameters or system parameters or indices as the feature vectors of a system in damage detection in an easy way. The SRM considered a more general theory for the non-parametric description of system state.

New Approach for Solving Master Equations in Quantum Optics and Quantum Statistics by Virtue of Thermo-Entangled State Representation

By introducing a fictitious mode to be a counterpart mode of the system mode under review we introduce the entangled state representation （η｜, which can arrange master equations of density operators p（t） in quantum statistics as state-vector evolution equations due to the elegant properties of （η｜. In this way many master equations （respectively describing damping oscillator, laser, phase sensitive, and phase diffusion processes with different initial density operators） can be concisely solved. Specially, for a damping process characteristic of the decay constant k we find that the matrix element of p（t） at time t in 〈η｜ representation is proportional to that of the initial po in the decayed entangled state （ηe^-kt｜ representation, accompanying with a Gaussian damping factor. Thus we have a new insight about the nature of the dissipative process. We also set up the so-called thermo-entangled state representation of density operators, ρ = f（d^2η/π）（η｜ρ〉D（η）, which is different from all the previous known representations.

Explicit solution of diffusion master equation under the action of linear resonance force via the thermal entangled state representation

Using the well-behaved features of the thermal entangled state representation, we solve the diffusion master equation under the action of a linear resonance force, and then obtain the infinitive operator-sum representation of the density operator. This approach may also be effective for treating other master equations. Moreover, we find that the initial pure coherent state evolves into a mixed thermal state after passing through the diffusion process under the action of the linear resonance force.

Relationship Between Wave Function and Corresponding Wigner Function Studied in Entangled State Representation

By using the explicit form of the entangled Wigner operator and the entangled state representation we derive the relationship between wave function and corresponding Wigner function for bipartite entangled systems. The technique of integration within an ordered product （IWOP） of operators is employed in our discussions.

Multipartite State Representations in Multi-mode Fock Space and Their Squeezing Transformations

We present the continuous state vector of the total coordinate of multi-partlcle and the state vector of their total momentum, respectively, which possess completeness relation in multi-mode Fock space by virtue of the integration within an order product （IWOP） technique. We also calculate the transition from classical transformation of variables in the states to quantum unitary operator, deduce a new multi-mode squeezing operator, and discuss its squeezing effect. In progress, it indicates that the IWOP technique provides a convenient way to construct new representation in quantum mechanics.

Application of Bipartite and Tripartite Entangled State Representations in Quantum Teleportation of Continuous Variables

We mostly investigate two schemes. One is to teleport a multi-mode W-type entangled coherent state using a peculiar bipartite entangled state as the quantum channel different from other proposals. Based on our formalism,teleporting multi-mode coherent state or squeezed state is also possible. Another is that the tripartite entangled state is used as the quantum channel of controlled teleportation of an arbitrary and unknown continuous variable in the case of three participators.

Quantum mechanical photoncount formula derived by entangled state representation

By introducing the thermo entangled state representation, we derive four new photocount distribution formulas for a given light field density operator. It is shown that these new formulas, which are convenient to calculate the photocount, can be expressed as integrations over a Laguree Gaussian function with a characteristic function, Wigner function, Q-function and P-function, respectively.

Deformation of Superoperator's Kraus Representation Derived by Weyl Correspondence and Entangled State Representation

By virtue of the Weyl correspondence and based on the the technique of integration within an ordered product of operators, we show under what condition the superoperator＇s Kraus representation p^1=∑μAμpA^＋μ can be deformed as p＇= （1/π） ∫ d^2d^2α（α）D（α）D（α）pD^＋（α）, where D（α） is the displacement operator, B（α） is a probability density related to the classical Weyl correspondence of Aμ. An alternate discussion by using the entangled state representation and through a quantum teleportation process is also presented.

Wave function for the squeezed atomic coherent state in entangled state representation and some of its applications

Based on the Einstein, Podolsky, and Rosen （EPR） entangled state representation, this paper introduces the wave function for the squeezed atomic coherent state （SACS）, which turns out to be just proportional to a single-variable ordinary Hermite polynomial of order 2j. As important applications of the wave function, the Wigner function of the SACS and its marginal distribution are obtained and the eigenproblems of some Hamiltonians for the generalized angular momentum system are solved.

Establishing path integral in the entangled state representation for Hamiltonians in quantum optics

Based on two mutually conjugate entangled state representations, we establish the path integral formalism for some Hamiltonians of quantum optics in entangled state representations. The Wigner operator in the entangled state representation is presented. Its advantages are explained.

Photon-number distribution of two-mode squeezed thermal states by entangled state representation

Using the entangled state representation, we convert a two-mode squeezed number state to a Hermite polynomial excited squeezed vacuum state. We first analytically derive the photon number distribution of the two-mode squeezed thermal states. It is found that it is a Jacobi polynomial; a remarkable result. This result can be directly applied to obtaining the photon number distribution of non-Gaussian states generated by subtracting from （adding to） two-mode squeezed thermal states.

New Formulation of Weyl Quantization Scheme in Coherent State Representation

By virtue of the technique of integration within an ordered product of operators we present a new formulation of the Weyl quantization scheme in the coherent state representation, which not only brings convenience for calculating the Weyl correspondence of normally ordered operators, but also directly leads us to find both the coherent state representation and the Weyl ordering representation of the Wigner operator.

Squeeze-swapping by Bell measurement studied in terms of the entangled state representation

By virtue of the entangled state representation （Hong-Yi Fan and J R Klauder 1994 Phys. Rev. A 49 704） and the two-mode squeezing operator＇s natural representation （Hong-Yi Fan and Yue Fan 1996 Phys. Rev. A 54 958） we propose the squeeze-swapping mechanism which can generate quantum entanglement and new squeezed states of continuum variables.

On Common Eigenvector of Parametric Interaction Hamiltonian and Number-Difference Operator Derived by Virtue of Entangled State Representation

By virtue of the properties of bipartite entangled state representation we derive the common eigenvector of the parametric Hamiltonian and the two-mode number-difference operator. This eigenvector is superposition of some definite two-mode Foek states with the coefficients being proportional to hypergeometric functions. The Gauss contiguous relation of hypergeometrie functions is used to confirm the formal solution.

Hermitian Operators Conjugate to Two-Mode Number-Difference Operator Studied in Entangled State Representation

In similar to the derivation of phase angle operator conjugate to the number operator by Arroyo Carrasco-Moya Cessay we deduce the Hermitian phase operators that are conjugate to the two-mode number-difference operatorand the three-mode number combination operator.It is shown that these operators are on the same footing in theentangled state representation as the one of Turski in the coherent state representation.

Some New Properties of Wigner Function Studied in Entangled State Representation

Based on the Wigner operator in the entangled state representation we study some new important propertiesof Wigner function for bipartite entangled systems,such as size of an entangled state,upper bound of Wigner functions,etc.These discussions demonstrate the beauty and elegance of the entangled state representation.

Entangled State Representation for Four-Wave Mixing

We introduce the entangled state representation to describe the four-wave mixing.We find that the four- wave mixing operator,which engenders the correct input-output field transformation,has a natural representation in the entangled state representation.In this way,we see that the four-wave mixing process not only involves squeezing but also is an entanglement process.This analysis brings convenience to the calculation of quadrature-amplitude measurement for the output state of four-wave mixing process.

Single-mode quadrature-amplitude measurement for generalized two-mode squeezed states studied by virtue of the entangled state representation

The result of one-mode quadrature-amplitude measurement for some generalized two-mode squeezed states has been studied by virtue of the entangled state representation of the corresponding two-mode squeezing operators. We find that the remaining fleld-mode simultaneously collapses to the single-mode squeezed state with more stronger squeezing. The measurement result caused by a single-mode squeezed state projector is also calculated, which indicates quantum entanglement in squeezing.

Four-Particle Entangled State Representation and Its Squeezing Transformation

The four-particle EPR entangled state 【 p, X2,X3,X4 】 is constructed. Thecorresponding quantum mechanical operator with respect to the classical transformation p → e~(λ1)p, X2 → e~(λ2)X2, X3 → e~(λ3) X3, and X4 → ee~(λ4) X4 in the state 【 p, X2, X3, X4 】 isinvestigated, and the four-mode realization of the S U(1, 1) Lie algebra as well as thecorresponding squeezing operators are presented.