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Communications in Theoretical Physics 2009年第4期51卷 729-742页

作者： FAN Hong-Yi hu li-yun Department of Physics Shanghai Jiao Tong University Shanghai 200030 China Department of Material Science and Engineering University of Science and Technology of China Hefei 230026 China

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.

关键词： master equation fictitious mode thermo-entangled state representation damping oscillator and laser phase sensitive and phase diffusion processes

Teleportation of Squeezed Entangled State

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Communications in Theoretical Physics 2007年第5期47卷 805-810页

作者： hu li-yun ZHOU Nan-Run Department of Physics Shanghai Jiao Tong University Shanghai 200030 China Department of Electronics Information Engineering Nanchang University Nanchang 330029 China

Based on the coherent entangled state ｜a, x〉 we introduce the squeezed entangled state （SES）. Then we propose a teleportation protocol for the SES by using Einstein-Podolsky-Rosen entangled state ｜η〉 as a quantum channel. The calculation is greatly simplified by virtue of the Schmidt decompositions of both ｜a, x〉 and ｜η〉. Any bipartite states that can be expanded in terms of ｜a, x〉 may be teleported in this way due to the completeness of ｜a, x〉.

关键词： squeezed entangled state continuous variables EPR state teleportation

Two-Variable Hermite Polynomial Excitation of Two-Mode Squeezed Vacuum State as Squeezed Two-Mode Number State

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Communications in Theoretical Physics 2008年第10期50卷 965-970页

作者： hu li-yun FAN Hong-Yi Department of Physics Shanghai Jiao Tong University Shanghai 200030 China

We find that the squeezed two-mode number state is just a two-variable Hermite polynomial excitation of thetwo-mode squeezed vacuum state (THPES).We find that the Wigner function of THPES and its marginal distributionsare just related to two-variable Hermite polynomials (or Laguerre polynomials) and that the tomogram of THPES canbe expressed by one-mode Hermite polynomial.

关键词： Two variable Hermite polynomial excitation state Wigner function marginal distribution tomgram

New Operator Realization of Superoperators and Its Application in Quantum Information Theory

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Communications in Theoretical Physics 2009年第7期52卷 37-40页

作者： FAN Hong-Yi hu li-yun Department of Physics Shanghai Jiao Tong University Shanghai 200030 China College of Physics and Communication Electronics Jiangxi Normal University Nanchang 330022 China Department of Material Science and Engineering University of Science and Technology of China Hefei 230026 China

By exposing deficiency of the usual superoperators that have no explicit operator-expression in quantuminformation theory we introduce thermo entangled state representation to endow each of these superoperators a definiteoperator-expression in an enlarged space in which one mode is a *** helps us to directly derive the role ofexponential of superoperators and the solutions of some master equations.

关键词： superoperators operator-expression thermo entangled state

New Convenient Way for Deriving Exponential Operators' Disentangling Formulas and Their Applications(Ⅱ)

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Communications in Theoretical Physics 2009年第2期51卷 506-508页

In the preceding paper [Commun. Theor. Phys. 51 （2009） 321] we have recommended a convenient method for disentangling exponential operators in the form of exp{B ＋ C}, trying to find an operator A that satisfies [A, B] = C, and [A, [A, B]] = 0, then from the Baker-Hausdorff formula we have exp{B ＋C} ： exp（B ＋ [A, B]} = e^A e^B e^-A. After arranging e^Ae^B = e^B e^A e^W, the disentangling exp{B ＋ C} = e^B e^W is obtained. In this work we use this method to two-mode case, especially, derive the normal ordering form of exp[h（a^＋a ＋ b^＋b）＋ ga^＋b^＋＋ kab] without appealing to lie algebra method.

关键词： exponential operator disentangling generalized two-mode squeezing operator

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Quantum Optical Squeezing Transform for Generalizing Fractional Fourier Transform

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Communications in Theoretical Physics 2008年第10期50卷 951-954页

作者： hu li-yun FAN Hong-Yi Department of Physics Shanghai Jiao Tong University Shanghai 200030 China

By establishing the relation between the optical scaled fractional Fourier transform （FFT） and quantum mechanical squeezing-rotating operator transform, we employ the bipartite entangled state representation of two-mode squeezing operator to extend the scaled FFT to more general cases, such as scaled complex FFT and entangled scaled FFT. The additiyity and eigenmodes are presented in quantum version. The relation between the scaled FFT and squeezing-rotating Wigner operator is studied.

关键词： squeezing transform scaled fractional Fourier transform IOWP technique

A Generalized Hankel Transformation Derived by Parametrized Entangled State Representations

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Communications in Theoretical Physics 2008年第7期50卷 85-88页

作者： FAN Hong-Yi hu li-yun Department of Physics Shanghai Jiao Tong University Shanghai 200030 China

Using the parametrized entangled state representations we have found a generalized Hankel transformationwith the integral kernel being a combination of Bessel *** generalized Hankel transformation corresponds tothe ap... 详细信息

关键词： parametrized bipartite entangled state generalized Hankel transformation

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

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Communications in Theoretical Physics 2008年第10期50卷 879-882页

作者： hu li-yun FAN Hong-Yi Department of Physics Shanghai Jiao Tong University Shanghai 200030 China Department of Material Science and Engineering University of Science and Technology of China Hefei 230026 China

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.

关键词： Weyl correspondence entangled state representation superoperator Kraus representation

Weyl Ordering Operator Formula Derived by IWOP Technique and Its Application for Fresnel Operator

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Communications in Theoretical Physics 2009年第11期52卷 840-844页

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... 详细信息

关键词： Weyl ordering operator IWOP technique Fresnel operator

Calculation of Gaussian Perturbation on Two Harmonic Oscillators by Virtue of Entangled State Representation

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Communications in Theoretical Physics 2007年第4X期48卷 629-632页

作者： hu li-yun ZHOU Nan-Run FAN Hong-Yi Department of Physics Shanghai Jiao Tong University Shanghai 200030 China Department of Electronics Information Engineering Nanchang University Nanchang 330029 China

The exact expressions of Gaussian-perturbation matrix elements in one- and two-mode Fock states are derived by virtue of the technique of integration within an ordered product of operators and the entangled state representation. It turns out that the matrix elements are just related to Gegenbauer polynomial and Hypergeometric function respectively. The 1st- and 2nd-order corrections to the energy levels and the 1st-order correction to wave functions of harmonic oscillator are deduced.

关键词： harmonic oscillator Gaussian perturbation IWOP technique