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The balanced homodyne detection as a readout scheme of gravitational-wavedetectors is carefully examined, which specifies the directly measured quantumoperator in the detection. This specification is necessary to apply the quantummeasurement theory to gravitational-wave detections. We clarify thecontribution of vacuum fluctuations to the noise spectral density without usingthe two-photon formulation. We found that the noise spectral density in thetwo-photon formulation includes vacuum fluctuations from the maininterferometer but does not includes those from the local oscillator whichdepends on the directly measured operators.

Vacuum fluctuations and balanced homodyne detection through ideal multi-mode photon number or power counting detectors