Multimode squeezed vacuum
= Multimode squeezed vacuum
{title2=$|0\rangle=C\exp(\tfrac12a'{}^\dagger M a'{}^\dagger)|0'\rangle$}
For an invertible finite-mode <Bogoliubov transformation> $a=Aa'+Ba'{}^\dagger$, the symmetric squeezing matrix is $M=-A^{-1}B$. The <canonical commutation relations> make its singular values strictly less than one. The normalized state has $|C|=\det(I-MM^\dagger)^{1/4}$. Infinitely many modes additionally require <bosonic mode mixing implementability>.