Two-mode SU(2) quadratic canonical operators and bipartite-entangled state representations for deriving complex fractional Fourier transformation

Nan-Run Zhou; Li-Yun Hu; Hong-Yi Fan

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Two-mode SU(2) quadratic canonical operators and bipartite-entangled state representations for deriving complex fractional Fourier transformation

机译：用于导出复分数阶傅里叶变换的双模SU（2）二次规范算子和二分纠缠态表示

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We demonstrate that the complex fractional Fourier transformation (CFRFT) can be deduced by two-mode SU(2) quadratic canonical operators and bipartite-entangled state representations. It turns out that the CFRFT is a special case of the two-dimensional (2D) complex Fresnel transformation, just as the 1D fractional Fourier transformation is adapted to the 1D Fresnel transformation.

机译：我们证明了复分数阶傅里叶变换（CFRFT）可以通过二模SU（2）二次规范运算符和二分纠缠态表示来推导。事实证明，CFRFT是二维（2D）复杂菲涅尔变换的特例，就像一维分数阶傅里叶变换适合于一维菲涅尔变换一样。

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《Physica Scripta: An International Journal for Experimental and Theoretical Physics》 |2009年第3期|共5页
作者
Nan-Run Zhou; Li-Yun Hu; Hong-Yi Fan;
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正文语种 eng
中图分类物理学;
关键词
Two-mode SU(2) quadratic; bipartite-entangled state; the complex fractional Fourier transformation;

机译：二次SU（2）二次;二元纠缠态;复分数阶傅里叶变换;

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1. Two-mode SU(2) quadratic canonical operators and bipartite-entangled state representations for deriving complex fractional Fourier transformation [J] . Nan-Run Zhou, Li-Yun Hu, Hong-Yi Fan Physica Scripta: An International Journal for Experimental and Theoretical Physics . 2009,第3期

机译：用于导出复分数阶傅里叶变换的双模SU（2）二次规范算子和二分纠缠态表示
2. Time Evolution Caused by Hamiltonian Composed of Quadratic Combination of Canonical Operators and Time-Dependent Two-Mode Fresnel Operator [J] . FAN Hong-Yi, LU Hai-Liang Communications in Theoretical Physics . 2006,第4期

机译：由规范算子和时间相关的双模菲涅耳算子的二次组合的哈密顿量引起的时间演化
3. Time Evolution Caused by Hamiltonian Composed of Quadratic Combination of Canonical Operators and Time-Dependent Two-Mode Fresnel Operator [J] . FAN Hong-Yi, LU Hai-Liang 理论物理通讯（英文版） . 2006,第010期

机译：由规范算子和时间相关的双模菲涅耳算子的二次组合的哈密顿量引起的时间演化
4. Digital computation of fractional Fourier and linear canonical transforms and sparse image representation [C] . Aykut Koc, Haldun M. Ozaktas, Burak Bartan, Asia-Pacific Signal and Information Processing Association Annual Summit and Conference . 2017

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5. Unitary and Hermitian fractional operators and their extensions: Fractional Mellin transform, joint fractional representations and fractional correlations. [D] . Akay, Olcay. 2000

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6. Complex dynamics and control of a novel physical model using nonlocal fractional differential operator with singular kernel [O] . A.E. Matouk, I. Khan 2020

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7. Multiscale discrete approximations of Fourier integral operators associated with canonical transformations and caustics [O] . Van De Hoop Maarten, Uhlmann Gunther, Vasy Andras, 2013

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8. Canonical Construction of Differential Operators Intertwining Representations of Real Semisimple Lie Groups [R] . Dobrev, V. K. 1986

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Two-mode SU(2) quadratic canonical operators and bipartite-entangled state representations for deriving complex fractional Fourier transformation

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