ABSTRACT: Using the Bloch-Messiah reduction we show that squeezing is an "irreducible" resource which remains invariant under transformations by linear optical elements. In particular, this gives 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 creating 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 nondemolition coupling of quadrature-phase amplitudes.