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Correspondence between quantum-optical transform and classical-optical transform explored by developing Dirac＇s symbolic method

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Frontiers of physics 2012年第3期7卷 261-310页

作者： Hong-yi Fan li-yun hu Department of Physics Shanghai Jiao Tong UniversityShanghai 200030China College of Physics&Communication Electronics Jiangxi Normal UniversityNanchang 330022China Department of Material Science and Engineering University of Science and Technology of China Hefei 230026 China

By virtue of the new technique of performing integration over Dirac＇s ket-bra operators, we ex- plore quantum optical version of classical optical transformations such as optical Fresnel transform, Hankel transform, fractional Fourier transform, Wigner transform, wavelet transform and Fresnel- Hadmard combinatorial transform etc. In this way one may gain benefit for developing classical optics theory from the research in quantum optics, or vice-versa. We cannot only find some new quantum mechanical unitary operators which correspond to the known optical transformations, de- riving a new theorem for calculating quantum tomogram of density operators, but also can reveal some new classical optical transformations. For examples, we find the generalized Fresnel opera- tor （GFO） to correspond to the generalized Fresnel transform （GFT） in classical optics. We derive GFO＇s normal product form and its canonical coherent state representation and find that GFO is the loyal representation of symplectic group multiplication rule. We show that GFT is just the transformation matrix element of GFO in the coordinate representation such that two successive GFTs is still a GFT. The ABCD rule of the Gaussian beam propagation is directly demonstrated in the context of quantum optics. Especially, the introduction of quantum mechanical entangled state representations opens up a new area in finding new classical optical transformations. The complex wavelet transform and the condition of mother wavelet are studied in the context of quantum op- tics too. Throughout our discussions, the coherent state, the entangled state representation of the two-mode squeezing operators and the technique of integration within an ordered product （IWOP） of operators are fully used. All these have confirmed Dirac＇s assertion：＂...for a quantum dynamic system that has a classical analogue, unitary transformation in the quantum theory is the analogue of contact transformation in the classical theory＂.

关键词： Dirac's symbolic method IWOP technique entangled state of continuum variables entangled Fresnel transform Collins formula Generalized Fresnel operator complex wavelet trans-form complex Wigner transform complex fractional Fourier transform symplectic wavelet trans-form entangled symplectic wavelet transform Symplectic-dilation mixed wavelet transform frac-tional Radon transform new eigenmodes of fractional Fourier transform

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Evolution of the single-mode squeezed vacuum state in amplitude dissipative channel

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Frontiers of physics 2014年第1期9卷 74-81页

作者： Hong-Yi Fan Shuai Wang li-yun hu Department of Physics Ningbo University Ningbo 315211 China School of Mathematics and Physics Changzhou University Changzhou 213164 China Department of Physics Jiangxi Normal University Nanchang 330022 China

Using the way of deriving infinitive sum representation of density operator as a solution to the master equation describing the amplitude dissipative channel by virtue of the entangled state representation, we show manifestly how the initial density operator of a single-mode squeezed vacuum state evolves into a definite mixed state which turns out to be a squeezed chaotic state with decreasing-squeezing and deeoherence. We investigate average photon number, photon statistics distributions for this mixed state.

关键词： single-mode squeezed vacuum decoherence entangled state representation sum repre-sentation

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Evolution of quantum states via Weyl expansion in dissipative channel

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Chinese Physics B 2019年第8期28卷 160-166页

作者： li-yun hu Zhi-Ming Rao Qing-Qiang Kuang Center for Quantum Science and Technology Jiangxi Normal UniversityNanchang 330022China Key Laboratory of Optoelectronic and Telecommunication Jiangxi Normal UniversityNanchang 330022China

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 *** is shown that they can be related by a transformation matrix corresponding to the unitary *** addition,for any density operator going through a dissipative channel,the evolution formula of the Wigner function is also *** applications,we considered further the two-mode squeezed vacuum as inputs,and obtained the resulted Wigner function and density operator within normal ordering *** 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.

关键词： Weyl expansion Wigner operator similar transformation two-mode squeezed state integration within ordered product(IWOP)technique

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3D entangled fractional squeezing transformation and its quantura mechanical correspondence

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Frontiers of physics 2016年第3期11卷 81-87页

作者： Fang Jia Shuang Xu Cheng-Zhi Deng Cun-Jin liu li-yun hu Center for Quantum Science and Technology Jiangxi Normal University Nanchan9 330022 China Department of Material Science and Engineering University of Science and Technology of China Hefei 230026 China School of Information Engineering Nanchang Institute of Technology Nanchang 330099 China

A new type of entangled fractionaJ squeezing transformation （EFrST） has been theoretically pro- posed for 2D entanglement [Front. Phys. 10, 100302 （2015）]. In this paper, we shall extend this case to that of 3D entanglement by introducing a type of three-mode entangled state representation, which is not the product of tkrec 1D cases. Using the technique of integration within an ordered product of operators, we derive a compact unitary operator corresponding to the 3D fractional entangling transformation, which is an entangling operator that presents a clear transformation re- lation. We also verified that the additivity property of the novel 3D EFrST is of a Fourier character by using its quantum mechanical description. As an application of this representation, the EFrST of the three-mode number state is calculated using the quantum description of the EFrST.

关键词： entangled fractional squeezing transformation entangled state representation

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Quantum speed limit for mixed states in a unitary system

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Chinese Physics B 2022年第11期31卷 236-243页

作者： Jie-hui huang li-Guo Qin Guang-Long Chen li-yun hu Fu-Yao liu School of Mathematics Physics and StatisticsShanghai University of Engineering ScienceShanghai 201620China College of Physics and Communication Electronics Jiangxi Normal UniversityNanchang 330022China

Since the evolution of a mixed state in a unitary system is equivalent to the joint evolution of the eigenvectors contained in it,we could use the tool of instantaneous angular velocity for pure states to study the quantum speed limit(QSL)of a mixed *** derive a lower bound for the evolution time of a mixed state to a target state in a unitary system,which automatically reduces to the quantum speed limit induced by the Fubini–Study metric for pure *** computation of the QSL of a degenerate mixed state is more complicated than that of a non-degenerate mixed state,where we have to make a singular value decomposition(SVD)on the inner product between the two eigenvector matrices of the initial and target *** combing these results,a lower bound for the evolution time of a general mixed state is *** order to compare the tightness among the lower bound proposed here and lower bounds reported in the references,two examples in a single-qubit system and in a single-qutrit system are studied analytically and numerically,*** conclusions derived in this work are independent of the eigenvalues of the mixed state,which is in accord with the evolution properties of a quantum unitary system.

关键词： quantum speed limit instantaneous angular velocity singular value decomposition

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A generalized two-mode entangled state： Its generation,properties, and applications

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Frontiers of physics 2014年第4期9卷 451-459页

作者： Kai-Min Zheng Shi-You liu Hao-liang Zhang Cun-Jin liu li-yun hu Center for Quantum Science and Technology College of Physics and Communication Electronics Jiangxi Normal University Nanchang 330022 China Key Laboratory of Optoelectronic and Telecommunication of Jiangxi Nanchang 330022 China

Using the technique of integration within an ordered product of operators we construct a generalized two-mode entangled state, which can be generated by an asymmetrical beam splitter （BS）. Some important properties of this state, such as orthogonality and Schmidt decomposition, are also dis- cussed by deriving the expression of BS operator in coordinate representation. As its applications, to conjugate state, obtain operator identities, generate new squeezing operators （squeezed state） are also presented. It is shown that the fidelity of quantum teleportation can be enhanced under certain case by using the asymmetrical new squeezed state as entangled resource.

关键词： entangled state beam splitter (BS) quantum teleportation

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Quantifying quantum correlation via quantum coherence

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Frontiers of physics 2018年第4期13卷 285-290页

作者： Guang-Yong Zhou lin-Jian huang Jun-Ya Pan li-yun hu Jie-hui huang College of Physics and Communication Electronics Jiangxi Normal University Nanchang 330022 China

Resource theory is applied to quantify the quantum correlation of a bipartite state and a computable measure is proposed. Since this measure is based on quantum coherence, we present another possible physical meaning for quantum correlation, i.e., the minimum quantum coherence achieved under local unitary transformations. This measure satisfies the basic requirements for quantifying quantum cor- relation and coincides with concurrence for pure states. Since no optimization is involved in the final definition, this measure is easy to compute irrespective of the Hilbert space dimension of the bipartite state.

关键词： resource theory quantum correlation quantum coherence

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Breeding of Zhongyouza 8, a Canola Variety with Large Seeds and High Oil Yield

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Agricultural Sciences in China 2006年第4期5卷 257-264页

作者： li yun-chang hu Qiong MEI De-sheng li Ying-de XU Yu-song Institute of Oil Crop Research Chinese Academy of Agricultural Sciences/National Center for Oil Crops Improvement/Key Laboratory for Oil Crops Improvement of Ministry of Agriculture Wuhan 430062 P.R.China

High oil yield resulted from a combination of high grain yield and high oil content is a prerequisite for the high efficient oilseed rape production. By using irradiation induced mutation and sexual hybridization combined with paired test cross, the fertility, yield and oil content of the three lines of cytoplasmic male sterility have been improved and a new hybrid variety Zhongyouza 8 with high oil yield was developed. It has been testified that the yield of Zhongyouza 8 was significantly higher than that of the control variety Zhongyou 821 with 9.82 and 10.64% increase in the regional trials of hubei Province and nationwide, respectively. The oil content and oil yield of Zhongyouza 8 were the highest among all the lines involved in hubei provincial trials, being 42.77% and 1 051.05 kg ha^-1 which was raised by 3% and 161.25 kg ha^-1 compared to the control Zhongyou 821, respectively. The genetic basis for the strong heterosis, and the factors contributing to the yield and oil content increase of Zhongyouza 8 as well as the strategy for high oil yielding variety improvement through increasing seed size were also discussed in this paper.

关键词： Brassica napus high oil yielding Zhongyouza 8 hybrid breeding

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Entanglement of coherent superposition of photon-subtraction squeezed vacuum

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Frontiers of physics 2017年第5期12卷 159-169页

作者： Cun-Jin liu Wei Ye Wei-Dong Zhou Hao-liang Zhang Jie-hui huang li-yun hu Center for Quantum Science and Technology Jiangxi Normal University Nanchang 330022 China

A new kind of non-Gaussian quantum state is introduced by applying nonlocal coherent superposition （τa＋ sb）^m of photon subtraction to two single-mode squeezed vacuum states, and the properties of entanglement are investigated according to the degree of entanglement and the average fidelity of quantum teleportation. The state can be seen as a single-variable Hermitian polynomial excited squeezed vacuum state, and its normalization factor is related to the Legendre polynomial. It is shown that, for τ = s, the maximum fidelity can be achieved, even over the classical limit （1/2）, only for even- order operation m and equivalent squeezing parameters in a certain region. However, the maximum entanglement can be achieved for squeezing parameters with a π phase difference. These indicate that the optimal realizations of fidelity and entanglement could be different from one another. In addition, the parameter τ/s has an obvious effect on entanglement and fidelity.

关键词： non-Gaussian operation quantum entanglement squeezed state

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Continuous-variable quantum key distribution based on photon addition operation

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Chinese Physics B 2021年第6期30卷 126-132页

作者： Xiao-Ting Chen Lu-Ping Zhang Shou-Kang Chang huan Zhang li-yun hu Center for Quantum Science and Technology Jiangxi Normal UniversityNanchang 330022China Key Laboratory of Optoelectronic and Telecommunication Jiangxi Normal UniversityNanchang 330022China

It is shown that the non-Gaussian operations can not only be used to prepare the nonclassical states, but also to improve the entanglement degree between Gaussian states. Thus these operations are naturally considered to enhance the performance of continuous variable quantum key distribution(CVQKD), in which the non-Gaussian operations are usually placed on the right-side of the entangled source. Here we propose another scheme for further improving the performance of CVQKD with the entangled-based scheme by operating photon-addition operation on the left-side of the entangled *** is found that the photon-addition operation on the left-side presents both higher success probability and better secure key rate and transmission distance than the photon subtraction on the right-side, although they share the same maximal tolerable noise. In addition, compared to both photon subtraction and photon addition on the right-side, our scheme shows the best performance and the photon addition on the right-side is the worst.

关键词： non-Gaussian operations continuous variable quantum key distribution photon-addition operation

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