  We study in detail a system of two interferometers aimed to the detection of
extremely faint phase-fluctuations. This system can represent a breakthrough
for detecting a faint correlated signal that would remain otherwise
undetectable even using the most sensitive individual interferometric devices,
that are limited by the shot noise. If the two interferometers experience
identical phase-fluctuations, like the ones introduced by the so called
"holographic noise", this signal should emerge if their output signals are
correlated, while the fluctuations due to shot noise and other independent
contributions will vanish. We show how the injecting quantum light in the free
ports of the interferometers can reduce the photon noise of the system beyond
the shot-noise, enhancing the resolution in the phase-correlation estimation.
We analyze both the use of two-mode squeezed vacuum or twin-beam state (TWB)
and of two independent squeezing states. Our results basically confirms the
benefit of using squeezed beams together with strong coherent beams in
interferometry, even in this correlated case. However, mainly we concentrate on
the possible use of TWB, discovering interesting and probably unexplored areas
of application of bipartite entanglement and in particular the possibility of
reaching in principle surprising uncertainty reduction.
