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Controllability of Quantum Systems with SU(1, 1) Dynamical Symmetry

WU Jianwu · WU Rebing · ZHANG Jing · LI Chunwen   

  1. WU Jianwu
    Beijing Aerospace Automatic Control Institute, Beijing 100854, China. Email: wujianwu@tsinghua.org.cn.
    WU Rebing · ZHANG Jing · LI Chunwen
    Department of Automation, Tsinghua University, Beijing 100084, China; Center for Quantum Information Science and Technology, BNRist, Beijing 100084, China.
    Email: rbwu@tsinghua.edu.cn; Jing-zhang@tsinghua.edu.cn; lcw@tsinghua.edu.cn.
  • Online:2021-06-25 Published:2021-03-11

WU Jianwu · WU Rebing · ZHANG Jing · LI Chunwen. Controllability of Quantum Systems with SU(1, 1) Dynamical Symmetry[J]. Journal of Systems Science and Complexity, 2021, 34(3): 827-842.

This paper presents sufficient and necessary conditions for the propagator controllability of a class of infinite-dimensional quantum systems with SU(1, 1) dynamical symmetry through the isomorphic mapping to the non-unitary representation of SU(1, 1). The authors prove that the elliptic condition of the total Hamiltonian is both necessary and sufficient for the controllability and strong controllability. The obtained results can be also extended to control systems with SO(2, 1) dynamical symmetry.

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