  The balanced homodyne detection as a readout scheme of gravitational-wave
detectors is carefully examined, which specifies the directly measured quantum
operator in the detection. This specification is necessary to apply the quantum
measurement theory to gravitational-wave detections. We clarify the
contribution of vacuum fluctuations to the noise spectral density without using
the two-photon formulation. We found that the noise spectral density in the
two-photon formulation includes vacuum fluctuations from the main
interferometer but does not includes those from the local oscillator which
depends on the directly measured operators.
