  We show that squeezing is an irreducible resource which remains invariant
under transformations by linear optical elements. In particular, we give a
decomposition of any optical circuit with linear input-output relations into a
linear multiport interferometer followed by a unique set of single mode
squeezers and then another multiport interferometer. Using this decomposition
we derive a no-go theorem for superpositions of macroscopically distinct states
from single-photon detection. Further, we demonstrate the equivalence between
several schemes for randomly creating polarization-entangled states. Finally,
we derive minimal quantum optical circuits for ideal quantum non-demolition
coupling of quadrature-phase amplitudes.
