What is Quantum Metrology and the Role of Quantum Entanglement

Measurement is one of the most significant aspects of physical sciences. The precision of measurement is associated with the advancement of mankind's civilization in certain aspects. For instance, the improvement in measuring lengths with feet, hands, steps to measuring with vernier calipers, microscope, laser ranging devices are witnessed. High precision measurements of physical parameters have been a dream for scientists and engineers for decades. All the time scientists are trying to get the perfect measurement of parameters, for example, distance, displacement, especially in optical phenomena like optical path length and optical phase measurement. The measurement procedure can be broken down into three stages: the experimental setup, the experimental process (doing the experiment), and then reading the scales on the experimental setup. Statistical or systematic errors are responsible for reducing the precision in the measurement and may be caused due to insufficient control of the probes or maybe arise due to environmental situations. Whatever the situation is, the error can be reduced by repeating the experiment several times and taking averages of the results. For the search of well-précised measurements, scientists have reached to use effects of quantum mechanics to reduce the errors in their measurements. Since, quantum theory has been the most successful theory for describing phenomena at the atomic and subatomic dimensions throughout history. It goes without saying, that measurement is one of the key factors in the advancement of mankind's society as, if one can measure up to some accuracy so that concept can be further research visualize very well. To better understand and research nature and the universe, researchers and scientists have put their attention to improving measurements. In this regard, they have developed a very weird theory now we call it the theory of quantum mechanics which is one of the most successful theories in history. The classical measurements were limited by the so-called shot-noise limit, which is nothing but vacuum fluctuations and can be removed or manipulated with proper advanced theory. Quantum metrology uses the resources of quantum mechanics to overcome this standard quantum limit. In this theory, researchers are using various photonic quantum states including coherent states, number states, NOON states, and entangled states. It has been well studied that a coherent state is a more classical state, and it reported in various research articles that through coherent states one can only achieve the classical limit. However, to make entanglement of coherent states it is reported recently that the shot-noise limit was beaten, and the ultimate limit was achieved called Heisenberg's limit. Similarly, NOON states are maximally entangled states and have shown better interest towards the ultimate limit, however, experimentally it is very difficult to achieve the ultimate limit due to the fragility of NOON states. So, in conclusion, we can say that quantum entanglement has played a vital role in the area of quantum metrology and has achieved the ultimate limit of precision currently researchers are working on different states including squeezed states to develop the best route for quantum metrological tasks. Quantum metrology's current focus is on quantum phase estimation, quantum imaging, quantum state, process estimates, and so on. Quantum phase estimation uses a non-classical light field to estimate any phase or phase shift with accuracy, surpassing the typical quantum limit or shot noise scaling. For instance, suppose one wants to determine the phase of N photons. Because of the shot noise fluctuations of the photons, if these N particles are in the classical field, the accuracy will be restricted by the standard quantum limit. The precision could be intensified, and the standard quantum limit would be overcome if the photons are correlated quantum mechanically. To go beyond standard quantum limit or shot noise limit, scientists have tried squeezed states for the high precision measurement of optical phase in the 1980s. My current focus is using squeezed states of light for the problem of quantum metrology, which are already been used in LIGO for the detection of gravitational waves.