Weak-value metrology refers to quantum measurement with a weak measurement process and post-selection. The outcome, called weak values, can be amplified beyond the eigenvalues of the observable; however, there is some debate on the usefulness of weak-value metrology in increasing the sensitivity of a gravitational wave detector. In this thesis, we investigated the sensitivity limit with regard to quantum shot noise and radiation pressure noise. For this purpose, we formulated an input-output
relation with a model via weak-value metrology, which allowed us to understand the optical processes under a condition wherein the weak value is applied intuitively. However, we found that the sensitivity of the modified model was not improved as the modified model destroyed the symmetry of the interferometer, which contributed to additional noise. Despite signal amplification, increasing sensitivity to detect more gravitational wave events is more vital.

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