We point out a new route to deducing integration formulas, i.e., using the technique of integration within an ordered product （IWOP） of operators we derive some new integration formulas, which seems concise. As a by...We point out a new route to deducing integration formulas, i.e., using the technique of integration within an ordered product （IWOP） of operators we derive some new integration formulas, which seems concise. As a by-product, some new operator identities also appear.展开更多
Starting from the optical fractional Fourier transform (FFT) and using the technique of integration withinan ordered product of operators we establish a formalism of FFT for quantum mechanical wave functions. In doing...Starting from the optical fractional Fourier transform (FFT) and using the technique of integration withinan ordered product of operators we establish a formalism of FFT for quantum mechanical wave functions. In doing so, theessence of FFT can be seen more clearly, and the FFT of some wave functions can be derived more directly and concisely.We also point out that different FFT integral kernels correspond to different quantum mechanical representations. Theyare generalized FFT. The relationship between the FFT and the rotated Wigner operator is studied by virtue of theWeyl ordered form of the Wigner operator.展开更多
Using the technique of integral within an ordered product (IWOP) of operators we show that the wavelet transform can be recasted to a matrix element of squeezing-displacing operator between the mother wavelet state ve...Using the technique of integral within an ordered product (IWOP) of operators we show that the wavelet transform can be recasted to a matrix element of squeezing-displacing operator between the mother wavelet state vector and the state vector to be transformed in the context of quantum mechanics. In this way many quantum optical states'wavelet transform can be easily derived.展开更多
Using the technique of integration within an ordered product of operators and the intermediate coordinatemomentum representation in quantum optics, as well as the excited squeezed state we derive a new form of Legendr...Using the technique of integration within an ordered product of operators and the intermediate coordinatemomentum representation in quantum optics, as well as the excited squeezed state we derive a new form of Legendre polynomials.展开更多
We introduce the quantum Hadamard operator in continuum state vector space and find that it can be decomposed into a single-mode squeezing operator and a position-momentum mutual transform operator. The two-mode Hadam...We introduce the quantum Hadamard operator in continuum state vector space and find that it can be decomposed into a single-mode squeezing operator and a position-momentum mutual transform operator. The two-mode Hadamard operator in bipartite entangled state representation is also introduced, which involves the two-mode squeezing operator and [η〉 ←→｜ξ〉 mutual transformation operator, where [η〉 and ｜ξ〉 are mutual conjugate entangled states. All the discussions are proceeded by virtue of the IWOP technique.展开更多
The q-analogues of two-mode squeezed states are introduced by virtue of deformation quantization methods and the technique of integration within an ordered product （IWOP） of operators. Some new completeness relation...The q-analogues of two-mode squeezed states are introduced by virtue of deformation quantization methods and the technique of integration within an ordered product （IWOP） of operators. Some new completeness relations about these squeezed states composed of the bra and ket which are not mutually Hermitian conjugates are obtained. Furthermore, the antibunching effects of the two-mode squeezed vacuum state S＇s（τ） │00） are investigated. It is found that, in different ranges of the squeezed parameter τ, both modes of the state exhibit the antibunching effects and the two modes of the state are always nonclassical correlation.展开更多
Using the technique of integration within an antinormally ordered product of operators we present a convenient approach for deriving some new operator identities in quantum optics theory. Based on P-representation we ...Using the technique of integration within an antinormally ordered product of operators we present a convenient approach for deriving some new operator identities in quantum optics theory. Based on P-representation we also derive a new formula for evaluating photocount distribution.展开更多
Using the coherent state representation we derive some new operator identities and study some mathematical relations in comblnatorics. The technique of integral within an ordered product （IWOP） of operators plays an...Using the coherent state representation we derive some new operator identities and study some mathematical relations in comblnatorics. The technique of integral within an ordered product （IWOP） of operators plays an essential role in realizing our goal.展开更多
Based on the technique of integration within an ordered product of operators, the Weyl ordering operator formula is derived and the Fresnel operators＇ Weyl ordering is also obtained, which together with the Weyl tran...Based on the technique of integration within an ordered product of operators, the Weyl ordering operator formula is derived and the Fresnel operators＇ Weyl ordering is also obtained, which together with the Weyl transformation can immediately lead to Eresnel transformation kernel in classical optics.展开更多
By virtue of the technique of integration within an ordered product of operators and the fundamentaloperator identity Hn(X) = 2n : Xn :, where X is the coordinate operator and Hn is the n-order Hermite polynomials,:: ...By virtue of the technique of integration within an ordered product of operators and the fundamentaloperator identity Hn(X) = 2n : Xn :, where X is the coordinate operator and Hn is the n-order Hermite polynomials,:: is the normal ordering symbol, we not only simplify the derivation of the main properties of Hermite polynomials,but also directly derive some new operator identities regarding to Hn(X). Operation for transforming f(X) → :f(X) :is also discussed.展开更多
We present a convenient approach to finding multi-partite entangled state with continuum variables, which is the common eigenvectors of center-of-mass coordinate and mass-weighted relative momenta, by decomposing the ...We present a convenient approach to finding multi-partite entangled state with continuum variables, which is the common eigenvectors of center-of-mass coordinate and mass-weighted relative momenta, by decomposing the normally ordered Gaussian-form operator expressing the completeness relation which is constructed by analyzing the eigenvector equations. The whole derivation is based on the technique of integration within an ordered product of operators.展开更多
We present a general formalism for setting up unitary transform operators from classical transforms via the technique of integration within an ordered product of operators, their normally ordered form can be obtained ...We present a general formalism for setting up unitary transform operators from classical transforms via the technique of integration within an ordered product of operators, their normally ordered form can be obtained too.展开更多
By virtue of the technique of integration within an ordered product of operators and the Schmidt decomposition of the entangled state |η〉, we reduce the general projection calculation in the theory of quantum telepo...By virtue of the technique of integration within an ordered product of operators and the Schmidt decomposition of the entangled state |η〉, we reduce the general projection calculation in the theory of quantum teleportation to a as simple as possible form and present a general formalism for teleportating quantum states of continuous variable.展开更多
We show that for tomographic approach there exist two mutual conjugate quantum states [p,σ, τ） and [x,μ, ν） （named the intermediate coordinate-momentum representation）, and the two Radon transforms of the Wign...We show that for tomographic approach there exist two mutual conjugate quantum states [p,σ, τ） and [x,μ, ν） （named the intermediate coordinate-momentum representation）, and the two Radon transforms of the Wigner operator are just the pure-state density matrices [p）σ1τσ1τ （p｜ and （p）λ,ν,λ,ν,（x｜ respectively. As a result, the tomogram of quantum states can be considered as the module-square of the states＇ wave function in these two representations. Throughout the paper we fully employ the technique of integration within an ordered product of operators. In this way we establish a new convenient formalism of quantum tomogram.展开更多
基金＊Supported by the National Natural Science Foundation of China under Grant No. 10775097, and the Natural Science Foundation of Heze University of Shandong Province, under Crant No. XY07WL01
文摘We point out a new route to deducing integration formulas, i.e., using the technique of integration within an ordered product （IWOP） of operators we derive some new integration formulas, which seems concise. As a by-product, some new operator identities also appear.
文摘Starting from the optical fractional Fourier transform (FFT) and using the technique of integration withinan ordered product of operators we establish a formalism of FFT for quantum mechanical wave functions. In doing so, theessence of FFT can be seen more clearly, and the FFT of some wave functions can be derived more directly and concisely.We also point out that different FFT integral kernels correspond to different quantum mechanical representations. Theyare generalized FFT. The relationship between the FFT and the rotated Wigner operator is studied by virtue of theWeyl ordered form of the Wigner operator.
文摘Using the technique of integral within an ordered product (IWOP) of operators we show that the wavelet transform can be recasted to a matrix element of squeezing-displacing operator between the mother wavelet state vector and the state vector to be transformed in the context of quantum mechanics. In this way many quantum optical states'wavelet transform can be easily derived.
文摘Using the technique of integration within an ordered product of operators and the intermediate coordinatemomentum representation in quantum optics, as well as the excited squeezed state we derive a new form of Legendre polynomials.
基金The project supported by National Natural Science Foundation of China under Grant No.10475056
文摘We introduce the quantum Hadamard operator in continuum state vector space and find that it can be decomposed into a single-mode squeezing operator and a position-momentum mutual transform operator. The two-mode Hadamard operator in bipartite entangled state representation is also introduced, which involves the two-mode squeezing operator and [η〉 ←→｜ξ〉 mutual transformation operator, where [η〉 and ｜ξ〉 are mutual conjugate entangled states. All the discussions are proceeded by virtue of the IWOP technique.
基金Project supported by the National Natural Science Foundation of China (Grant No 10574060)the Natural Science Foundation of Liaocheng University of China (Grant No X071049)
文摘The q-analogues of two-mode squeezed states are introduced by virtue of deformation quantization methods and the technique of integration within an ordered product （IWOP） of operators. Some new completeness relations about these squeezed states composed of the bra and ket which are not mutually Hermitian conjugates are obtained. Furthermore, the antibunching effects of the two-mode squeezed vacuum state S＇s（τ） │00） are investigated. It is found that, in different ranges of the squeezed parameter τ, both modes of the state exhibit the antibunching effects and the two modes of the state are always nonclassical correlation.
基金Supported by the National Natural Science Foundation of China under Grant Nos. 10775097 and 10874174
文摘Using the technique of integration within an antinormally ordered product of operators we present a convenient approach for deriving some new operator identities in quantum optics theory. Based on P-representation we also derive a new formula for evaluating photocount distribution.
基金The project supported by National Natural Science Foundation of China under Grant No. 10475056
文摘Using the coherent state representation we derive some new operator identities and study some mathematical relations in comblnatorics. The technique of integral within an ordered product （IWOP） of operators plays an essential role in realizing our goal.
基金Supported by the National Natural Science Foundation of China under Grant No.10475056the Research Foundation of the Education Department of Jiangxi Province
文摘Based on the technique of integration within an ordered product of operators, the Weyl ordering operator formula is derived and the Fresnel operators＇ Weyl ordering is also obtained, which together with the Weyl transformation can immediately lead to Eresnel transformation kernel in classical optics.
文摘By virtue of the technique of integration within an ordered product of operators and the fundamentaloperator identity Hn(X) = 2n : Xn :, where X is the coordinate operator and Hn is the n-order Hermite polynomials,:: is the normal ordering symbol, we not only simplify the derivation of the main properties of Hermite polynomials,but also directly derive some new operator identities regarding to Hn(X). Operation for transforming f(X) → :f(X) :is also discussed.
基金Supported by the National Natural Science Foundation of China under Grant No. 10874174the Specialized Research Fund for the Doctoral Program of Higher Education under Grant No. 20070358009
文摘We present a convenient approach to finding multi-partite entangled state with continuum variables, which is the common eigenvectors of center-of-mass coordinate and mass-weighted relative momenta, by decomposing the normally ordered Gaussian-form operator expressing the completeness relation which is constructed by analyzing the eigenvector equations. The whole derivation is based on the technique of integration within an ordered product of operators.
基金The project supported by National Natural Science Foundation of China under Grant No. 10475056
文摘We present a general formalism for setting up unitary transform operators from classical transforms via the technique of integration within an ordered product of operators, their normally ordered form can be obtained too.
文摘By virtue of the technique of integration within an ordered product of operators and the Schmidt decomposition of the entangled state |η〉, we reduce the general projection calculation in the theory of quantum teleportation to a as simple as possible form and present a general formalism for teleportating quantum states of continuous variable.
基金The project supported by National Natural Science Foundation of China under Grant No. 10475056 and the Specialized Research Fund for the Doctorial Progress of Higher Education under Grant No. 20040358019
文摘We show that for tomographic approach there exist two mutual conjugate quantum states [p,σ, τ） and [x,μ, ν） （named the intermediate coordinate-momentum representation）, and the two Radon transforms of the Wigner operator are just the pure-state density matrices [p）σ1τσ1τ （p｜ and （p）λ,ν,λ,ν,（x｜ respectively. As a result, the tomogram of quantum states can be considered as the module-square of the states＇ wave function in these two representations. Throughout the paper we fully employ the technique of integration within an ordered product of operators. In this way we establish a new convenient formalism of quantum tomogram.
