共查询到20条相似文献,搜索用时 15 毫秒
1.
Based on our previous paper (Commun. Theor. Phys. 39 (2003) 417) we derive the convolution theorem of fractional Fourier
transformation in the context of quantum mechanics, which seems a convenient
and neat way. Generalization of this method to the complex fractional
Fourier transformation case is also possible. 相似文献
2.
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. 相似文献
3.
HU Li-Yun FAN Hong-Yi 《理论物理通讯》2008,50(10):951-954
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. 相似文献
4.
Fractional Fourier transforms, which are related to chirp and wavelet transforms, lead to the notion of fractional Fourier domains. The concept of filtering of signals in fractional domains is developed, revealing that under certain conditions one can improve upon the special cases of these operations in the conventional space and frequency domains. Because of the ease of performing the fractional Fourier transform optically, these operations are relevant for optical information processing. 相似文献
5.
Based on the newly constructed two mutually conjugate 3-mode entangled states of continuum variablesin three-mode Fock space we introduce entangled fractional Fourier transform (EFFT) for the tripartite entangled staterepresentations, which are not a direct product of three 1-dimensional FFTs. The eigenmodes of EFFT are obtained,which is different from the usual Hermite polynomials. The EFFT of the three-mode squeezed state is derived. 相似文献
6.
We deduce entangled fractional Fourier transformation (EFFT) for
the multipartite entangled state representation, which was newly
constructed with two mutually conjugate n-mode entangled states of
continuum variables in n-mode Fock space. We establish a formalism
of EFFT for quantum mechanical wave functions, which provides
us a convenient way to derive some wave functions. We find that
the eigenmode of EFFT is different from the usual Hermite Polynomials.
We also derive the EFFT of the n-mode squeezed state. 相似文献
7.
分数傅立叶变换的进展与展望 总被引:3,自引:1,他引:2
在综合国内外有关文献的基础上,评述分数傅立叶变换在信息光学中的新进展。概述分数傅立叶变换的发展过程,并对其研究现状进行了简略总结,同时对其未来的发展作出展望。 相似文献
8.
FANHong-Yi JIANGNian-Quan 《理论物理通讯》2003,40(1):39-44
Based on the newly constructed two mutually conjugate 3-mode entangled states of continuum variables in three-mode Fock space we introduce entangled fractional Fourier transform (EFFT) for the tripartite entangled state representations, which are not a direct product of three 1-dimensional FFTs. The eigenmodes of EFFT are obtained,which is different from the usual Hermite polynomials. The EFFT of the three-mode squeezed state is derived. 相似文献
9.
By applying the Fourier slice theorem, Sθ(λ) =∫^∞-∞Pθ(t)e^-iλt=F(λcosθ,λsinθ),where Pθ(t) is a projection of f(x,p)=^∞∫∫-∞F(u,v)e^i(uz+up) dudv along lines of constant, to the Wigner operator we are naturally led to a projection operator (pure state), which results in a new complete representation. The Weyl orderimg formalism of the Wigner operator is used in the derivation. 相似文献
10.
11.
Hari M. Srivastava Waseem Z. Lone Firdous A. Shah Ahmed I. Zayed 《Entropy (Basel, Switzerland)》2022,24(10)
The discrete Fourier transform is considered as one of the most powerful tools in digital signal processing, which enable us to find the spectrum of finite-duration signals. In this article, we introduce the notion of discrete quadratic-phase Fourier transform, which encompasses a wider class of discrete Fourier transforms, including classical discrete Fourier transform, discrete fractional Fourier transform, discrete linear canonical transform, discrete Fresnal transform, and so on. To begin with, we examine the fundamental aspects of the discrete quadratic-phase Fourier transform, including the formulation of Parseval’s and reconstruction formulae. To extend the scope of the present study, we establish weighted and non-weighted convolution and correlation structures associated with the discrete quadratic-phase Fourier transform. 相似文献
12.
FAN Hong-Yi JIANG Nian-Quan 《理论物理通讯》2004,42(7)
We show that for n-dimensional complex fractional Fourier transform the corresponding complex fractional Radon transform can also be derived, however, it is different from the direct product of two n-dimensional real fractional Radon transforms. The complex fractional Radon transform of two-mode Wigner operator is calculated. 相似文献
13.
By applying the Fourier slice theorem, Sθ(λ) =∫_{-\infty }^{\infty }Pθ(t)e-iλt=F(λcosθ,λsinθ), where Pθ(t) is a projection of f( x,p) =∫∫_{-\infty}^{\infty }F( u,v) ei(ux+vp)ldudv along lines of constant, to the Wigner operator we are naturally led to projection operator (pure state), which results in a new complete epresentation. The Weyl orderimg formalism of the Wigner operator is used in the derivation. 相似文献
14.
FANHong-Yi JIANGNian-Quan 《理论物理通讯》2004,42(1):23-26
We show that for n-dimensional complex fractional Fourier transform the corresponding complex fractional Radon transform can also be derived, however, it is different from the direct product of two n-dimensional real fractional Radon transforms. The complex fractional Radon transform of two-mode Wigner operator is calculated. 相似文献
15.
分析了联合广义分数傅里叶变换相关器相关峰的特性,得到通过改变广义分数傅里叶变换的系统参量可以提高广义分数相关峰性能的结论.进行了数值模拟和光学实验,并根据两者的结果对四个相关峰的性能指标相关峰强度最大值、峰能比、识别能力、信噪比进行了比较分析,说明只要适当控制系统参量,联合广义分数傅里叶变换相关器比联合分数傅里叶变换相关器具有更好的相关性能,有助于提高光学相关器识别的准确率. 相似文献
16.
YU Zu-Rong 《理论物理通讯》2001,(10)
With the help of su(2) algebra technique, a new equivalent form of the fractional Fourier transformation is given. Two examples are illustrated for their physical application in quantum optics.`` 相似文献
17.
18.
This paper introduces Lorentz beams to describe certain laser
sources that produce highly divergent fields. The fractional Fourier
transform (FRFT) is applied to treat the propagation of Lorentz
beams. Based on the definition of convolution and the convolution
theorem of the Fourier transform, an analytical expression for a
Lorentz beam passing through a FRFT system has been derived. By
using the derived formula, the properties of a Lorentz beam in the
FRFT plane are illustrated numerically. 相似文献
19.
HUANG Da-Zu CHEN Zhi-Gang GUO Ying 《理论物理通讯》2009,51(2):221-226
A (n, n)-threshold scheme of multiparty quantum secret sharing of classical or quantum message is proposed based on the discrete quantum Fourier transform. In our proposed scheme, the secret message, which is encoded by using the forward quantum Fourier transform and decoded by using the reverse, is split and shared in such a way that it can be reconstructed among them only if all the participants work in concert. Fhrthermore, we also discuss how this protocol must be carefully designed for correcting errors and checking eavesdropping or a dishonest participant. Security analysis shows that our scheme is secure. Also, this scheme has an advantage that it is completely compatible with quantum computation and easier to realize in the distributed quantum secure computation. 相似文献
20.
针对常规傅里叶变换所不能解决的啁啾噪声滤除问题,利用Wigner分布函数分析分数傅里叶变换的空域和频域特性,提出在分数傅里叶变换域进行啁啾滤波的方法。并将该方法应用到图像处理中,对分数傅里叶变换滤除一维和二维图像的啁啾噪声进行了计算机仿真,获得了满意的效果,结果表明该方法在图像处理中的有效性。 相似文献