An important reason why LIGO can achieve such high precision is the use of compressed state light.
Before this, the accuracy of human-made interferometers was limited by the fluctuations of the vacuum state. This limit is called the standard quantum limit (also called the shot-noise limit): the accuracy of the interferometer is 1/1 of the input light intensity.
Inversely proportional to the power of 2.
But later scientists discovered that the standard quantum limit can be broken by inputting compressed state light into an interferometer.
Light in a compressed state can compress the uncertainty of its phase and amplify the uncertainty of its intensity. Conversely, it can also compress the uncertainty of its intensity and amplify the uncertainty of its phase.
Inputting the compressed state light that compresses the phase uncertainty into one port of the interferometer can compress the uncertainty of the phase difference between the two beams of light participating in the interference, and at the same time amplify the uncertainty of the pressure generated by the collision of the photon motion with the mirror.
The uncertainty in the phase difference of the compressed light enables the accuracy of interferometer measurements to exceed standard quantum limits.
For details, please refer to Phys. Rev. D 23, 1693 (1981).
At the same time, LIGO does not use an ordinary Michelson interferometer, but a Fabry-Perot-Michelson interferometer.
The main difference is that the interference arm uses an optical cavity, and the light oscillates in the cavity to increase the intensity of the light.
In addition, LIGO has also done a lot of work in data collection and processing (there are people in the LIGO team who specialize in signal processing).
Theoretically, the limits of human measurement accuracy are constrained only by Heisenberg's uncertainty principle.
The measurement accuracy limit obtained from the Heisenberg uncertainty principle is that the accuracy is inversely proportional to the light intensity. This limit is called the Heisenberg limit.
As technology advances, LIGO is moving towards this true quantum limit.