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An extension of the input-output relation for a conventional Michelsoninterferometric gravitational-wave detector is carried out to treat anarbitrary coherent state for the injected optical beam. This extension is oneof necessary researches toward the clarification of the relation betweenconventional gravitational-wave detectors and a simple model of agravitational-wave detector inspired by weak-measurements in [A.~Nishizawa,Phys. Rev. A {\bf 92} (2015), 032123.]. The derived input-output relationdescribes not only a conventional Michelson-interferometric gravitational-wavedetector but also the situation of weak measurements. As a result, we may saythat a conventional Michelson gravitational-wave detector already includes theessence of the weak-value amplification as the reduction of the quantum noisefrom the light source through the measurement at the dark port.

annals of physics

Extension of the input-output relation for a Michelson interferometer to  arbitrary coherent-state light sources: --- Gravitational-wave detector and  weak-value amplification ---