The two-mode squeezed even and odd coherent states are quantum states with some non-classical properties.The entanglement of two-mode squeezed even and odd coherent states are measured by non-classicality of P-functio...The two-mode squeezed even and odd coherent states are quantum states with some non-classical properties.The entanglement of two-mode squeezed even and odd coherent states are measured by non-classicality of P-functionand separability inequalities of EPR-operators.展开更多
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 func...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.展开更多
Pair coherent state, is a state of a two-mode radiation field that is known as a state with non-gaussian wave function. In this paper, study on the pair coherent state, we notice that with superposition of two first t...Pair coherent state, is a state of a two-mode radiation field that is known as a state with non-gaussian wave function. In this paper, study on the pair coherent state, we notice that with superposition of two first terms of this states, one two-qubits formed. Because of the importance of two-qubits in theory of quantum entanglement, with two different measures with the title of concurrence and D-concurrence, we have studied the amount of entanglement and discussed its details. At the end, we describe these measures for pair coherent states as a function of the amplitude of the SU（2） coherent states.展开更多
We reveal that the two-variable Hermite function hm,n, which is the generalized Bargmann representation of the two-mode Fock state, involves quantum entanglement of harmonic oscillator＇s wave functions. The Schmidt d...We reveal that the two-variable Hermite function hm,n, which is the generalized Bargmann representation of the two-mode Fock state, involves quantum entanglement of harmonic oscillator＇s wave functions. The Schmidt decomposition of hm,n is derived. It also turns out that hm,n can be generated by windowed Fourier transform of the single-variable Hermite functions. As an application, the wave function of the two-variable Hermite polynomial state S（γ）Hm,n （μa1^＋, μa2^＋│00〉, which is the minimum uncertainty state for sum squeezing, in （ η│representation is calculated.展开更多
In this paper,two-mode displaced excited squeezed vacuum states (TDESVS) are constructed and theirnormalization and completeness are investigated.Using the entangled state representation and Weyl ordering formof the W...In this paper,two-mode displaced excited squeezed vacuum states (TDESVS) are constructed and theirnormalization and completeness are investigated.Using the entangled state representation and Weyl ordering formof the Wigner operator,the Wigner functions of TDESVS are obtained and the variations of Wigner functions withthe parameters m,n and r are investigated.Besides,two marginal distributions of Wigner functions of TDESVS areobtained,which exhibit some entangled properties of the two-particle's system in TDESVS.展开更多
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 varia...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.展开更多
We construct the nonlinear tripartite entangled state representation and the related generalized Wigner operator. Then we discussed the Wigner functions of the nonlinear tripartite entangled state and the three-mode n...We construct the nonlinear tripartite entangled state representation and the related generalized Wigner operator. Then we discussed the Wigner functions of the nonlinear tripartite entangled state and the three-mode nonlinear squeezed vacuum state, and obtained the classical Weyl corresponding function of the three-mode nonlinear squeezed state.展开更多
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 ...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.展开更多
In this paper we set up quantum mechanical correspondence of the Poisson integral formula.We show that Poisson kernel function existing in the transformation between the continuum entangled state representation and it...In this paper we set up quantum mechanical correspondence of the Poisson integral formula.We show that Poisson kernel function existing in the transformation between the continuum entangled state representation and its induced state,i.e.the number-difference-correlated amplitude entangled state representation.展开更多
We calculate Wigner function, tomogram of the pair coherent state by using its Sehmidt decomposition in the coherent state representation. It turns out that the Wigner function can be seen as the quantum entanglement ...We calculate Wigner function, tomogram of the pair coherent state by using its Sehmidt decomposition in the coherent state representation. It turns out that the Wigner function can be seen as the quantum entanglement （QE） between two two-variable Hermite polynomials （TVHP） and the tomogram is further simplified as QE of two single-variable Hermite polynomials. The Husimi function of pair coherent state is also calculated.展开更多
Like the progress made by Dirac that wave function ψ(x) was reformed as x |ψ,where x| is the coordinate representation,we endow the characteristic function χλ = Tr(e λa-λaρ) of density operator ρ with the mean...Like the progress made by Dirac that wave function ψ(x) was reformed as x |ψ,where x| is the coordinate representation,we endow the characteristic function χλ = Tr(e λa-λaρ) of density operator ρ with the meaning of wave function of |ρ in the thermal entangled state η| representation in the doubled Fock space,χλ = η = λ|ρ,where |ρ = ρ|η = 0.We find the time evolution of χλ can then be directly and neatly obtained via this approach.The way of deriving the density operator from η = λ | ρ is also presented.展开更多
For entangled three particles one should treat their wave function as a whole.There is no physical meaning talking about the wave function(or Wigner function) for any one of the tripartite,and therefore considering th...For entangled three particles one should treat their wave function as a whole.There is no physical meaning talking about the wave function(or Wigner function) for any one of the tripartite,and therefore considering the entangled Wigner function(Wigner operator) is of necessity.In this paper,we introduce a pair of mutually conjugate tripartite entangled state representations for defining the Wigner operator of entangled tripartite.Its marginal distributions and the Wigner function of the three-mode squeezed vacuum state are presented.Deriving wave function from its corresponding tripartite entangled Wigner function is also discussed.Moreover,through establishing the n-mode entangled state representation,we introduce the n-mode entangled Wigner operator,which would be more generally useful in quantum physics.展开更多
Choosing I-concurrence as the measure of bipartite entanglement and using yon Neumann projective local measurements, localizable entanglement （LE） in a three-qutrit system is studied. A superposition of the qutrit-c...Choosing I-concurrence as the measure of bipartite entanglement and using yon Neumann projective local measurements, localizable entanglement （LE） in a three-qutrit system is studied. A superposition of the qutrit-coherent- state of this system is considered ant its LE is obtained and analyzed as a function of the relevant parameters. It is observed that one may achieve the maximal entanglement or no entanglement at all, depending on the choice of the parameters involved.展开更多
基金supported by the National Natural Science Foundation of China under Grant No 10674174Science Foundation of the Education Department of Liaoning Province under Grant No.05L151the Science and Technology Department of Shenyang under Grant No.1053115-1-8
文摘The two-mode squeezed even and odd coherent states are quantum states with some non-classical properties.The entanglement of two-mode squeezed even and odd coherent states are measured by non-classicality of P-functionand separability inequalities of EPR-operators.
基金Supported by the President Foundation of Chinese Academy of ScienceApecialized Research Fund for the Doctorial Progress of Higher EducationNational Natural Science Foundation of China under Grant Nos.10874174 and 10947017/A05
文摘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.
文摘Pair coherent state, is a state of a two-mode radiation field that is known as a state with non-gaussian wave function. In this paper, study on the pair coherent state, we notice that with superposition of two first terms of this states, one two-qubits formed. Because of the importance of two-qubits in theory of quantum entanglement, with two different measures with the title of concurrence and D-concurrence, we have studied the amount of entanglement and discussed its details. At the end, we describe these measures for pair coherent states as a function of the amplitude of the SU（2） coherent states.
文摘We reveal that the two-variable Hermite function hm,n, which is the generalized Bargmann representation of the two-mode Fock state, involves quantum entanglement of harmonic oscillator＇s wave functions. The Schmidt decomposition of hm,n is derived. It also turns out that hm,n can be generated by windowed Fourier transform of the single-variable Hermite functions. As an application, the wave function of the two-variable Hermite polynomial state S（γ）Hm,n （μa1^＋, μa2^＋│00〉, which is the minimum uncertainty state for sum squeezing, in （ η│representation is calculated.
基金Supported by the National Natural Science Foundation of China under Grant No.10574060Shandong Province of China under Grant No.Y2008A23Liaocheng University of China under Grant No.X071049
文摘In this paper,two-mode displaced excited squeezed vacuum states (TDESVS) are constructed and theirnormalization and completeness are investigated.Using the entangled state representation and Weyl ordering formof the Wigner operator,the Wigner functions of TDESVS are obtained and the variations of Wigner functions withthe parameters m,n and r are investigated.Besides,two marginal distributions of Wigner functions of TDESVS areobtained,which exhibit some entangled properties of the two-particle's system in TDESVS.
基金The project supported by National Natural Science Foundation of China under Grant No. 10475056 and the President Foundation of the Chinese Academy of Sciences
文摘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.
基金Open Foundation of Laboratory of High-intensity Optics，中国科学院资助项目
文摘We construct the nonlinear tripartite entangled state representation and the related generalized Wigner operator. Then we discussed the Wigner functions of the nonlinear tripartite entangled state and the three-mode nonlinear squeezed vacuum state, and obtained the classical Weyl corresponding function of the three-mode nonlinear squeezed state.
基金The project supported by The President Foundation of the Chinese Academy of Sciences
文摘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.
基金Supported by the National Natural Science Foundation of China under Grant No.10874174 the Specialized Reserach Fund for The Doctoral Progress of Higher Education of China under Grant No.20070358009
文摘In this paper we set up quantum mechanical correspondence of the Poisson integral formula.We show that Poisson kernel function existing in the transformation between the continuum entangled state representation and its induced state,i.e.the number-difference-correlated amplitude entangled state representation.
基金Supported by the National Natural Science Foundation of China under Grant Nos.10775097 and 10874174the Research Foundation of the Education Department of Jiangxi Province
文摘We calculate Wigner function, tomogram of the pair coherent state by using its Sehmidt decomposition in the coherent state representation. It turns out that the Wigner function can be seen as the quantum entanglement （QE） between two two-variable Hermite polynomials （TVHP） and the tomogram is further simplified as QE of two single-variable Hermite polynomials. The Husimi function of pair coherent state is also calculated.
基金supported by the National Natural Science Foundation of China (Grant No. 11175113)
文摘Like the progress made by Dirac that wave function ψ(x) was reformed as x |ψ,where x| is the coordinate representation,we endow the characteristic function χλ = Tr(e λa-λaρ) of density operator ρ with the meaning of wave function of |ρ in the thermal entangled state η| representation in the doubled Fock space,χλ = η = λ|ρ,where |ρ = ρ|η = 0.We find the time evolution of χλ can then be directly and neatly obtained via this approach.The way of deriving the density operator from η = λ | ρ is also presented.
基金supported by the Postdoctoral Science Foundation of Jiangsu Province (Grant No.1202012B)the Research Fund for Advanced Talents of Jiangsu University (Grant No.1281190029)
文摘For entangled three particles one should treat their wave function as a whole.There is no physical meaning talking about the wave function(or Wigner function) for any one of the tripartite,and therefore considering the entangled Wigner function(Wigner operator) is of necessity.In this paper,we introduce a pair of mutually conjugate tripartite entangled state representations for defining the Wigner operator of entangled tripartite.Its marginal distributions and the Wigner function of the three-mode squeezed vacuum state are presented.Deriving wave function from its corresponding tripartite entangled Wigner function is also discussed.Moreover,through establishing the n-mode entangled state representation,we introduce the n-mode entangled Wigner operator,which would be more generally useful in quantum physics.
文摘Choosing I-concurrence as the measure of bipartite entanglement and using yon Neumann projective local measurements, localizable entanglement （LE） in a three-qutrit system is studied. A superposition of the qutrit-coherent- state of this system is considered ant its LE is obtained and analyzed as a function of the relevant parameters. It is observed that one may achieve the maximal entanglement or no entanglement at all, depending on the choice of the parameters involved.
