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New generalized binomial theorems involving two-variable Hermite polynomials via quantum optics approach and their applications

  • Xiang-Guo MengEmail author
  • Jian-Ming Liu
  • Ji-Suo Wang
  • Hong-Yi Fan
Regular Article

Abstract

We extend the ordinary binomial theorem to the case which involves two-variable Hermite polynomials in the context of quantum optics, and analytically obtain several new generalized binomial theorems whose results exactly equal the single- or two-mode Hermite polynomials. As their applications in the field of quantum optics, we analytically prove that the multiple-photon-subtracted squeezed state ambnesab†+ra†+tb |00⟩ is equivalent to the Hermite-polynomial-weighted quantum state serving as an easily produced non-Gaussian entangled information resource, and the Wigner functions of spin coherent states and their marginal distributions are respectively the Laguerre polynomials and the Hermite polynomials.

Graphical abstract

Keywords

Quantum Optics 

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Copyright information

© EDP Sciences, SIF, Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Xiang-Guo Meng
    • 1
    • 2
    Email author
  • Jian-Ming Liu
    • 3
  • Ji-Suo Wang
    • 4
  • Hong-Yi Fan
    • 5
  1. 1.School of Physical Science and Information Engineering, Liaocheng UniversityLiaochengP.R. China
  2. 2.Shandong Provincial Key Laboratory of Optical Communication Science and Technology, Liaocheng UniversityLiaochengP.R. China
  3. 3.Department of ComputerWeifang Medical UniversityWeifangP.R. China
  4. 4.Shandong Provincial Key Laboratory of Laser Polarization and Information Technology, College of Physics and Engineering, Qufu Normal UniversityQufuP.R. China
  5. 5.Department of Material Science and EngineeringUniversity of Science and Technology of ChinaHefeiP.R. China

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