  Broadband quantum noise reduction can be achieved in gravitational wave
detectors by injecting frequency dependent squeezed light into the the dark
port of the interferometer. This frequency dependent squeezing can be generated
by combining squeezed light with external filter cavities. However, in future
long baseline interferometers (LBIs), the filter cavity required to achieve the
broadband squeezing has a low bandwidth -- necessitating a very long cavity to
mitigate the issue from optical loss. It has been shown recently that by taking
advantage of Einstein-Podolsky-Rosen (EPR) entanglement in the squeezed light
source, the interferometer can simultaneously act as a detector and a filter
cavity. This is an attractive broadband squeezing scheme for LBIs because the
length requirement for the filter cavity is naturally satisfied by the length
of the interferometer arms. In this paper we present a systematic way of
finding the working points for this broadband squeezing scheme in LBIs. We also
show that in LBIs, the EPR scheme achieves nearly perfect ellipse rotation as
compared to 4km interferometers which have appreciable error around the
intermediate frequency. Finally, we show that an approximation for the
opto-mechanical coupling constant in the 4km case can break down for longer
baselines. These results are applicable to future detectors such as the 10km
Einstein Telescope and the 40km Cosmic Explorer.
