= Particle-antiparticle two-mode squeezed vacuum
{title2=$|\psi\rangle=\sqrt{1-|q|^2}\sum_n(-q)^n|n,n\rangle$}
For a pair of distinct bosonic <particle> and <antiparticle> modes, the normalized state obeying $(a+qb^\dagger)|\psi\rangle=(b+qa^\dagger)|\psi\rangle=0$ is $\sqrt{1-|q|^2}\sum_{n\geq0}(-q)^n|n,n\rangle$, for $|q|<1$. It contains equal occupations and is generated by a pair-creation exponential. Infinite products require a separate implementability or regulator check.
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