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The fast progress in improving the sensitivity of the gravitational-wave (GW) detectors, we all have witnessed in the recent years, has propelled the scientific community to the point, when quantum behaviour of such immense measurement devices as kilometer-long interferometers starts to matter. The time, when their sensitivity will be mainly limited by the quantum noise of light is round the corner, and finding the ways to reduce it will become a necessity. Therefore, the primary goal we pursued in this review was to familiarize a broad spectrum of readers with the theory of quantum measurements in the very form it finds application in the area of gravitational-wave detection. We focus on how quantum noise arises in gravitational-wave interferometers and what limitations it imposes on the achievable sensitivity. We start from the very basic concepts and gradually advance to the general linear quantum measurement theory and its application to the calculation of quantum noise in the contemporary and planned interferometric detectors of gravitational radiation of the first and second generation. Special attention is paid to the concept of Standard Quantum Limit and the methods of its surmounting.
The quantum nature of the electromagnetic field imposes a fundamental limit on the sensitivity of optical precision measurements such as spectroscopy, microscopy, and interferometry. The so-called quantum limit is set by the zero-point fluctuations o
Space-based gravitational wave detectors based on the Laser Interferometer Space Antenna (LISA) design operate by synthesizing one or more interferometers from fringe velocity measurements generated by changes in the light travel time between three s
Earth-based gravitational-wave detectors will be limited by quantum noise in a large part of their spectrum. The most promising technique to achieve a broadband reduction of such noise is the injection of a frequency dependent squeezed vacuum state f
Long-baseline laser-interferometer gravitational-wave detectors are operating at a factor of 10 (in amplitude) above the standard quantum limit (SQL) within a broad frequency band. Such a low classical noise budget has already allowed the creation of
Future ground-based gravitational-wave detectors are slated to detect black hole and neutron star collisions from the entire stellar history of the universe. To achieve the designed detector sensitivities, frequency noise from the laser source must b