  We generalize a new approach to entanglement conditions for light of
undefined photons numbers given in [Phys. Rev. A {\bf 95}, 042113 (2017)] for
polarization correlations to a broader family of interferometric phenomena.
Integrated optics allows one to perform experiments based upon multiport
beamsplitters. To observe entanglement effects one can use multi-mode
parametric down-conversion emissions. When the structure of the Hamiltonian
governing the emissions has (infinitely) many equivalent Schmidt decompositions
into modes (beams), one can have perfect EPR-like correlations of numbers of
photons emitted into "conjugate modes" which can be monitored at spatially
separated detection stations. We provide entanglement conditions for
experiments involving three modes on each side, and three-input-three-output
multiport beamsplitters, and show their violations by bright squeezed vacuum
states. We show that a condition expressed in terms of averages of observed
rates is a much better entanglement indicator than a related one for the usual
intensity variables. Thus the rates seem to emerge as a powerful concept in
quantum optics, especially for fields of undefined intensities.
