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.

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.

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.

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.

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.

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.

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.

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.

Density matrix of two interacting particles with kinetic coupling derived in bipartite entangled state representation

A density matrix is usually obtained by solving the Bloch equation, however only a few Hamiltonians＇ density matrices can be analytically derived. The density matrix for two interacting particles with kinetic coupling is hard to derive by the usual method due to this coupling; this paper solves this problem by using the bipartite entangled state representation.

New operator identities with regard to the two-variable Hermite polynomial by virtue of entangled state representation

By virtue of the entangled state representation we concisely derive some new operator identities with regard to the two-variable Hermite polynomial （TVHP）. By them and the technique of integration within an ordered product （IWOP） of operators we further derive new generating function formulas of the TVHP. They are useful in quantum optical theoretical calculations. It is seen from this work that by combining the IWOP technique and quantum mechanical representations one can derive some new integration formulas even without really performing the integration.

New approach for analysing master equations of generalized phase diffusion models in the entangled state representation

By virtue of the well-behaved properties of the bipartite entangled states representation, this paper analyse and solves some master equations for generalized phase diffusion models, which seems concise and effective. This method can also be applied to solve other master equations.

Study Hankel Transforms and Properties of Bessel Function via Entangled State Representation Transformation in Quantum Mechanics

In Phys. Lett. A 313 （2003） 343 we have found that the self-recipràcal Hankel transformation （HT） is embodied in quantum mechanics by a transform between two entangled state representations of continuum variables. In this work we study Hankel transforms and properties of Bessel function via entangled state representations＇ transformation in quantum mechanics.

Complex-Variable Fokker-Planck Equation Solved in Entangled State Representation

We lind that the Fokker-Planck equation in complex variables can be conveniently solved in the context of bipartite entangled state representation and its relationship with SU（2） Lie algebraic generators＇ new realization {（1/4）[（Q1 - Q2）^2 ＋ （P1＋ P2）^2], （1/4）[（Q1 ＋Q2）^2＋ （P1 - P2）^2], and -（i/2）（Q1P2 ＋ Q2P1）}, the quadratic combination of canonical operators.

Inversion formula and Parseval theorem for complex continuous wavelet transforms studied by entangled state representation

In a preceding letter （2007 Opt. Lett. 32 554） we propose complex continuous wavelet transforms and found Laguerre-Gaussian mother wavelets family. In this work we present the inversion formula and Parseval theorem for complex continuous wavelet transform by virtue of the entangled state representation, which makes the complex continuous wavelet transform theory complete. A new orthogonal property of mother wavelet in parameter space is revealed.

Energy level formula for two moving charged particles with Coulomb coupling derived via the entangled state representations

This paper derives energy level formula for two moving charged particles with Coulomb coupling by making full use of two mutually conjugate entangled state representations. These newly introduced entangled state representations seem to provide a direct and convenient approach for solving certain dynamical problems for two-body systems.

Nonlinear two-mode squeezing obtained by analysing two-mode exponential quadrature operators in entangled state representation

By analysing the properties of two-mode quadratures in an entangled state representation （ESR） we derive from ESR some complicated exponential quadrature operators for nonlinear two-mode squeezing, which directly leads to wave function of the nonlinear squeezed state in ESR.