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    An algorithm for keeping unitary evolution of a wave function in time-dependent potential field
    Jiaying SONG, Guangjiong DONG
    Journal of East China Normal University(Natural Science)    2024, 2024 (3): 121-127.   DOI: 10.3969/j.issn.1000-5641.2024.03.013
    Abstract33)   HTML2)    PDF (1012KB)(8)      

    The numerical solution for wave function evolution plays an important role in quantum mechanics research. Many numerical algorithms have been developed for time-independent potential fields. However, multiple physical problems exist with the time-dependent potential. In this case, previously developed algorithms cannot guarantee the unitary evolution of wave function. In this study, the Crank-Nicolson algorithm to maintain unitary evolution in time-dependent potential fields is developed with a fourth-order accurate Numerov algorithm used to achieve high-precision spatial discretization. A numerical test demonstrates that the new algorithm maintains the unitarity and stability of wavefunction evolution.

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    Quantum parameter estimation and initial state optimization based on the Jaynes-Cummings model
    Liwen QIAO, Jiaxin PENG, Baiqiang ZHU, Keye ZHANG
    Journal of East China Normal University(Natural Science)    2024, 2024 (3): 128-135.   DOI: 10.3969/j.issn.1000-5641.2024.03.014
    Abstract42)   HTML2)    PDF (903KB)(35)      

    Quantum parameter estimation is a powerful theoretical tool for inferring unknown parameters in physical models from experimental data. The Jaynes-Cummings model is widely used in quantum optics, and describes the interaction between a two-level atom and a single-mode quantum optical field. Systematic research was performed on the estimation precision of atom-light coupling strength “g” in this model and the initial state was identified by which the estimation can achieve the best precision. Our results can improve the precision of quantum measurement with the Jaynes-Cummings model, and can be used for quantum metrology with other hybrid quantum systems.

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    E-payment protocol scheme based on quantum entanglement measurement theory
    Minhao ZHU, Lei MA
    Journal of East China Normal University(Natural Science)    2024, 2024 (3): 136-146.   DOI: 10.3969/j.issn.1000-5641.2024.03.015
    Abstract39)   HTML2)    PDF (761KB)(7)      

    An electronic payment protocol based on basic quantum mechanics is proposed. Some current loopholes in the classic payment systems pose security risks. The proposed scheme utilizes the correlations existing between entangled particles at the quantum level to implement the steps of signing, purchasing, and paying, whereby the validity of a signature is verified via quantum one-way functions and quantum SWAP test circuits. Payment information is transmitted through redundant particles in channel detection, thereby saving costs. Experimental results show that the proposed scheme has unconditional security as guaranteed by the basic principles of quantum mechanics and meets the basic requirements of payment systems.

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    Linear entropy uncertainty relation of Ising model under Dzyaloshinskii-Moriya interaction
    Yu ZHAO, Jinming LIU
    Journal of East China Normal University(Natural Science)    2024, 2024 (3): 147-155.   DOI: 10.3969/j.issn.1000-5641.2024.03.016
    Abstract28)   HTML2)    PDF (945KB)(7)      

    In this research, by considering the two-qubit Ising model under Dzyaloshinskii-Moriya(DM) interaction as the research object, we investigate the effects of coupling strength, DM interaction and ambient temperature on the linear entropy uncertainty relation(EUR) in the system. Meanwhile, the variation of thermal entanglement with environment with ambient temperature is also discussed, and the relationship between thermal entanglement and linear EUR is compared. The results demonstrate that the systemic linear entropy uncertainty and thermal entanglement variance trend depends on the selection of environmental parameters, and their overall evolution behavior is roughly anti-related. Additionally, for a complete set of mutually unbiased bases, when different measurement base combinations are selected, the uncertainty relation lower bound will vary with the change in the number of measurement bases; moreover, the linear EUR can be transformed into an equation in special cases and its lower bound does not depend on the selection of a specific observation quantity. Compared with the previous quantum memory-assisted EUR, it provides a useful reference for precise measurement.

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