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1.
The Fourier slice transformation of the Wigner operator and the quantum tomogram of the density operator 下载免费PDF全文
Using the Weyl quantization scheme and based on the Fourier slice transformation(FST) of the Wigner operator,we construct a new expansion formula of the density operator ρ,with the expansion coefficient being the FST of ρ’s classical Weyl correspondence,and the latter the Fourier transformation of ρ’s quantum tomogram.The coordinate-momentum intermediate representation is used as the Radon transformation of the Wigner operator. 相似文献
2.
New transformation of Wigner operator in phase space quantum mechanics for the two-mode entangled case 下载免费PDF全文
As a natural and important extension of Fan's paper (Fan Hong-Yi 2010 Chin. Phys. B 19 040305) by employing the formula of operators' Weyl ordering expansion and the bipartite entangled state representation this paper finds a new two-fold complex integration transformation about the Wigner operator Δ ( μ,v ) (in its entangled form) in phase space quantum mechanics, and its inverse transformation. In this way, some operator ordering problems regarding to ( a1+-a2) and (a1+a2+) can be solved and the contents of phase space quantum mechanics can be enriched, where ai,ai+ are bosonic creation and annihilation operators, respectively. 相似文献
3.
We find a new complex integration-transform which can establish a new relationship between a two-mode operator's matrix element in the entangled state representation and its Wigner function. This integration keeps modulus invariant and therefore invertible. Based on this and the Weyl–Wigner correspondence theory, we find a two-mode operator which is responsible for complex fractional squeezing transformation. The entangled state representation and the Weyl ordering form of the two-mode Wigner operator are fully used in our derivation which brings convenience. 相似文献
4.
According to Fan-Hu's formalism (Fan Hong-Yi and Hu Li-Yun 2009 Opt. Commun. bf282 3734) that the tomogram of quantum states can be considered as the module-square of the state wave function in the intermediate coordinate-momentum representation which is just the eigenvector of the Fresnel quadrature phase, we derive a new theorem for calculating quantum tomogram of density operator, i.e., the tomogram of a density operator ρ is equal to the marginal integration of the classical Weyl correspondence function of F+ρF, where F is the Fresnel operator. Applications of this theorem to evaluating the tomogram of optical chaotic field and squeezed chaotic optical field are presented. 相似文献
5.
By virtue of the Weyl ordering method,we find a new formalism of optical field operator expansion in number state representation.Miscellaneous optical fields’(coherent state,squeezed field,Wigner operator,etc.) new expansions are therefore exhibited.Some new generating functions of special polynomials are derived herewith. 相似文献
6.
The generalization of tomographic maps to hyperplanes is considered.
We find that the Radon transform of the Wigner operator in
multi-dimensional phase space leads to a normally ordered operator
in binomial distribution---a mixed-state density operator.
Reconstruction of the Wigner operator is also feasible. The normally
ordered form and the Weyl ordered form of the Wigner operator are
used in our derivation. The operator quantum tomography theory is
expressed in terms of some operator identities, with the merit
of revealing the essence of the theory in a simple and concise way. 相似文献
7.
8.
《中国物理 B》2019,(8)
Based on the Weyl expansion representation of Wigner operator and its invariant property under similar transformation, we derived the relationship between input state and output state after a unitary transformation including Wigner function and density operator. It is shown that they can be related by a transformation matrix corresponding to the unitary evolution. In addition, for any density operator going through a dissipative channel, the evolution formula of the Wigner function is also derived. As applications, we considered further the two-mode squeezed vacuum as inputs, and obtained the resulted Wigner function and density operator within normal ordering form. Our method is clear and concise, and can be easily extended to deal with other problems involved in quantum metrology, steering, and quantum information with continuous variable. 相似文献
9.
众所周知,量子态的演化可用与其相应的Wigner函数演化来代替.因为量子态的Wigner函数和量子态的密度矩阵一样,都包含了概率分布和相位等信息,因此对量子态的Wigner函数进行研究,可以更加快速有效地获取量子态在演化过程的重要信息.本文从经典扩散方程出发,利用密度算符的P表示,导出了量子态密度算符的扩散方程.进一步通过引入量子算符的Weyl编序记号,给出了其对应的Weyl量子化方案.另外,借助于密度算符的另一相空间表示-Wigner函数,建立了Wigner算符在扩散通道中演化方程,并给出了其Wigner算符解的形式.本文推导出了Wigner算符在量子扩散通道中的演化规律,即演化过程中任意时刻Wigner算符的形式.在此结论的基础上,讨论了相干态经过量子扩散通道的演化情况. 相似文献
10.
Xue-Fen Xu 《International Journal of Theoretical Physics》2010,49(7):1446-1451
In a preceding paper (Fan and Lv in J. Math. Phys. 50:102108, 2009), the phase-space integration corresponding to the straight line characteristic of two different real parameters λ,τ over the Wigner operator (i.e. the Radon transformation) leads to pure-state density operator |u〉
λ,τ
λ,τ
〈u|, where |u〉
λ,τ
is just the coordinate-momentum intermediate representation. In this work we show that generalized Radon transformation of
the Wigner operator yields multimode density operator of continuum variables. This provides us with a new approach for obtaining
multimode entangled state representation. The Weyl ordering of the Wigner operator is used in our discussions. 相似文献
11.
By introducing the generalized Wigner operator for s-parameterized quasiprobability distribution and employing the technique of integration within ordered product (IWOP) of operators (normally ordered, Weyl ordered or antinormally ordered), we derive two new quantum-mechanical formulas for describing no counts registered on a photonic detector when a light field’s density operator ρ is known, one involves ρ’s s-parameterized distribution function, and the other involves ρ’s coherent state mean value, when these information is known then using the new formulas to calculate no-photocount would be convenient. 相似文献
12.
Hong-yi Fan 《Optics Communications》2010,283(17):3296-3300
We discuss what happens to the Radon transformation of signal's Wigner functions (i.e., signal's Wigner transformation (WT)) if the signal function undergoes various optical processes, such as Fraunhofer diffraction, lens transformation and Fresnel diffraction, etc. Because the usual Wigner transforms can be studied via their corresponding transforms of the Wigner operator, we use the Weyl ordered form of the Wigner operator and the Weyl ordering invariance under similar transformations to derive the result, we find that the alteration of Radon transformation of signal's Wigner function (or named the variation of tomogram function), through these optical processes, can be ascribed to the variation of Radon transformation parameters once the parameter of WT is given. 相似文献
13.
Wen-jian Yu Ye-jun Xu Hong-chun Yuan Ji-suo Wang 《International Journal of Theoretical Physics》2011,50(9):2871-2877
We first deduce the s-ordered expansion of the Wigner operator. Since Radon transformation of Wigner operator is just the intermediate representation
|x〉
λ,ν projector, we naturally obtain the s-ordered product of |x〉
λ,νλ,ν〈x|. Accordingly, the completeness relation is still preserved under the s-ordering. Finally, based on it, we obtain the s-ordered expansion of some useful operator in quantum optics, and some new operator identities are revealed accordingly. 相似文献
14.
Based on the Fan-Hu's formalism, i.e., the tomogram of two-mode quantum states can be considered as the module square of the states' wave function in the intermediate representation, which is just the eigenvector of the Fresnel quadrature phase, we derive a new theorem for calculating the quantum tomogram of two-mode density operators, i.e., the tomogram of a two-mode density operator is equal to the marginal integration of the classical Weyl correspondence function of F2+ρF2, where F2 is the two-mode Fresnel operator. An application of the theorem in evaluating the tomogram of an optical chaotic field is also presented. 相似文献
15.
New two-fold integration transformation for the Wigner operator in phase space quantum mechanics and its relation to operator ordering 下载免费PDF全文
Using the Weyl ordering of operators expansion formula (Hong-Yi
Fan, \emph{ J. Phys.} A {\bf 25} (1992) 3443) this paper finds a
kind of two-fold integration transformation about the Wigner
operator $\varDelta \left( q',p'\right) $
($\mathrm{q}$-number transform) in phase space quantum mechanics,
$\iint_{-\infty}^{\infty}\frac{{\rm d}p'{\rm d}q'}{\pi
}\varDelta \left( q',p'\right) \e^{-2\i\left(
p-p'\right) \left( q-q'\right) }=\delta \left(
p-P\right) \delta \left( q-Q\right),$
and its inverse%
$
\iint_{-\infty}^{\infty}{\rm d}q{\rm d}p\delta \left( p-P\right)
\delta \left( q-Q\right) \e^{2\i\left( p-p'\right) \left(
q-q'\right) }=\varDelta \left(
q',p'\right),$ where $Q,$ $P$ are the coordinate
and momentum operators, respectively. We apply it to study mutual
converting formulae among $Q$--$P$ ordering, $P$--$Q$ ordering and Weyl
ordering of operators. In this way, the contents of phase space
quantum mechanics can be enriched. The formula of the Weyl
ordering of operators expansion and the technique of integration within the Weyl
ordered product of operators are used in this discussion. 相似文献
16.
Jun-hua Chen Hong-yi Fan Xu-bing Tang 《International Journal of Theoretical Physics》2012,51(1):14-22
It is known that beamsplitter can be used to produce quantum entanglement, in this paper we examine this topic from the point
of view of Wigner operators. Using Weyl-ordering of the Wigner operator and the Weyl ordering invariance of Weyl ordered operators
under similarity transformation we derive the entanglement rule of Wigner operators at a beamsplitter. 相似文献
17.
It is known that exp [iλ (Q1P1i/2)] is a unitary single-mode squeezing operator,where Q1,P1 are the coordinate and momentum operators,respectively.In this paper we employ Dirac’s coordinate representation to prove that the exponential operator S n ≡ exp [iλ sum((QiPi+1+Qi+1Pi))) from i=1 to n ],(Qn+1=Q1,Pn+1=P1),is an n-mode squeezing operator which enhances the standard squeezing.By virtue of the technique of integration within an ordered product of operators we derive S n ’s normally ordered expansion and obtain new n-mode squeezed vacuum states,its Wigner function is calculated by using the Weyl ordering invariance under similar transformations. 相似文献
18.
FAN Hong-Yi 《理论物理通讯》2004,41(2):205-208
Based on the technique of integral within a Weyl ordered product of
operators, we present applications of the Weyl ordered two-mode Wigner
operator for quantum mechanical entangled system, e.g., we derive the
complex Wigner transform and its relation to the complex fractional Fourier
transform, as well as the entangled Radon transform. 相似文献
19.
N.L. Balazs 《Physica A》1978,94(2):181-191
In the classical theory of Brownian motion we can consider the Langevin equation as an infinitesimal transformation between the coordinates and momenta of a Brownian particle, given probabilistically, since the impulse appearing is characterized by a Gaussian random process. This probabilistic infinitesimal transformation generates a streaming on the distribution function, expressed by the classical Fokker-Planck and Kramers-Chandrasekhar equations. If the laws obeyed by the Brownian particle are quantum mechanical, we can reinterpret the Langevin equation as an operator relation expressing an infinitesimal transformation of these operators. Since the impulses are independent of the coordinates and momenta we can think of them as c numbers described by a Gaussian random process. The so resulting infinitesimal operator transformation induces a streaming on the density matrix. We may associate, according to Weyl functions with operators. The function associated with the density matrix is the Wigner function. Expressing, then, these operator relations in terms of these functions we can express the streaming as a continuity equation of the Wigner function. We find that in this parametrization the extra terms which appear are the same as in the classical theory, augmenting the usual Wigner equation. 相似文献
20.
FAN Hong-Yi 《理论物理通讯》2003,40(10)
By virtue of the property that Weyl ordering is invariant under similar transformations we show that the Weyl ordered form of the Wigner operator, a Dirac δ-operator function, brings much convenience for derivingmiscellaneous Wigner transforms. The operators which engender various transforms of the Wigner operator, can alsobe easily deduced by virtue of the Weyl ordering technique. The correspondence between the optical Wigner transformsand the squeezing transforms in quantum optics is investigated. 相似文献