Squeezing is independent of the laser power used, so that's not really relevant here. Squeezed light is injected at the output port, where the photodetectors are. It is injected in the opposite direction to the classical light leaving the interferometer, where it mixes with the light field in the interferometer and has the effect of reducing quantum shot noise of the classical light that leaves.
In any case, I think you've confused the circulating light power with the input laser power. The circulating light power will eventually reach something like 1MW (currently it's lower) thanks to optical cavities, but the input laser power is actually only 50W (currently), eventually 125W.
