Abstract
We reveal that the two-variable Hermite function hm,n, whichis the generalized Bargmann representation of the two-mode Fock state, involvesquantum entanglement of harmonic oscillator's wave functions. The Schmidtdecomposition of hm,n is derived. It also turns out that hm,n canbe generated by windowed Fourier transform of the single-variable Hermitefunctions. As an application, the wave function of the two-variable Hermitepolynomial state S(r)Hm,n(μa1†,μa2†)|00⟩, which is the minimum uncertaintystate for sum squeezing, in ⟨η| representationis calculated.
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