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

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 a m b n e sa † b † + 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.