Describing two-mode squeezed-light experiments without two-mode entanglement or squeezing

In a recent work [Phys. Rev. A \textbf{102}, 053723 (2020)] we have shown that experiments that produce and characterize single-mode light squeezing can be explained in a way where no single-mode squeezed light state is produced in the setup. Here we apply the same ideas to demonstrate that experiments that produce and characterize two-mode light squeezing can also be explained without the production of two-mode squeezed light states. In particular, we show that there is no entanglement between the signal and idler ``twin beam'' modes. This fact may be surprising, since this setup is frequently used to implement entangled-based quantum information protocols such as quantum teleportation. Our work brings an alternative view of the phenomenon. We generalize the Luis and S\'anchez-Soto's two-mode relative phase distribution [Phys. Rev. A \textbf{53}, 495 (1996)] to treat four modes, showing that a general physical explanation for the noise reduction in the experiments is a better definition of a phase relation among the four involved optical modes: Signal, idler, and two local oscillators.