  The balanced homodyne detection as a readout scheme of gravitational-wave
detectors is carefully examined from the quantum field theoretical point of
view. The readout scheme in gravitational-wave detectors specifies the directly
measured quantum operator in the detection. This specification is necessary
when we apply the recently developed quantum measurement theory to
gravitational-wave detections. We examine the two models of measurement. One is
the model in which the directly measured quantum operator at the photodetector
is Glauber's photon number operator, and the other is the model in which the
power operator of the optical field is directly measured. These two are
regarded as ideal models of photodetectors. We first show these two models
yield the same expectation value of the measurement. Since it is consensus in
the gravitational-wave community that vacuum fluctuations contribute to the
noises in the detectors, we also clarify the contributions of vacuum
fluctuations to the quantum noise spectral density without using the two-photon
formulation which is used in the gravitational-wave community. We found that
the conventional noise spectral density in the two-photon formulation includes
vacuum fluctuations from the main interferometer but does not include those
from the local oscillator. Although the contribution of vacuum fluctuations
from the local oscillator theoretically yields the difference between the above
two models in the noise spectral densities, this difference is negligible in
realistic situations.
