  We examine the internal structure of two-mode entanglement criteria for
quadrature and number-phase squeezed states. (i) We first address entanglement
criteria obtained via partial transpose of Schrodinger-Robertson inequality,
where presence of an extra term makes them stronger. We show that this extra
term performs an optimization within two intra-mode rotations, for the
variables mixing in the entanglement criterion. We demonstrate this situation
both for quadrature and number-phase squeezed states. (ii) We realize that
Simon's criterion performs this optimization automatically. (iii) Hence, we
derive a Simon-like criterion for number-phase squeezed states which performs
this optimization in the number-phase plane. The method can be generalized also
for other states, e.g., amplitude-squeezed states. In addition to examining the
intra-mode rotations, (iv) we also present an entanglement scheme in terms of
product of the noises of the two modes, i.e., noise-area. We question,
analytically and numerically, whether the well-known entanglement criteria are
actually search mechanisms for a noise-area below unity. In this regard, we
also numerically show the following. We consider an entangled state. We
minimize the noise-area for the product form of the Duan-Giedke-Cirac-Zoller
criterion (Mancini {\it et. al.}) with respect to the intra-mode rotations. We
observe that this noise-area (actually) is the input nonclassicality that a
beam-splitter necessitates in order to generate exactly the amount of
entanglement our particular state possesses. (vi) Additionally, we define an
alternative entanglement measure for Gaussian states which can also be adapted
to multimode entanglement. We further raise some intriguing questions, e.g., on
the existence of an easier definition of an entanglement depth for number-phase
squeezed states.
