  A "squeezed-vacuum" state considered in quantum optics is shown to be
realized in the ground-state wavefunction for the bilayer quantum Hall system
at the total Landau level filling of $\nu=1/m$ (m: odd integer). This is
derived in the boson approximation, where a particle-hole pair creation across
the symmetric-antisymmetric gap, $\Delta_{SAS}$, is regarded as a boson. In
terms of the pseudospin describing the layers, the state is a spin-squeezed
state, where the degree of squeezing is controlled by the layer separation and
$\Delta_{SAS}$. An exciton condensation, which amounts to a rotated
spin-squeezed state, has a higher energy due to the degraded SU(2) symmetry for
$\Delta_{SAS} \neq 0$.
