Research progress in quantum precision measurements based on linear and nonlinear interferometers

Quantum precision measurement is based on the basic principle of quantum mechanics by using the interaction between light, atoms and magnetism to measure physical quantities, also known as precision measurements based on microscopic particle systems and their quantum states. As an important means of quantum precision measurement, interferometer precision measurement technology has great application value in quantum communication. The linear interferometer measures the magnitude of the physical quantity by using the phase change obtained from the measurements, but measurement accuracy is limited and unable to meet the requirements of today's scientific problems for the precision measurement of some physical quantities. On this basis, nonlinear interferometer is able to take advantage of the quantum entangled state, that is, using the two light fields of quantum correlation characteristics to realize quantum enhanced precision measurement, thus greatly improving the measurement sensitivity, Therefore, the scope of application is wider, but the preparation of quantum entangled states has many limitations in practical manipulation. With the maturity of experimental conditions and technology, how to use both of these interferometers to further improve the measurement accuracy of the phase signal so as to break the limitation to shot noise, breaking the standard quantum limit and even approaching to the Heisenberg limit has become a frontier research topic . In this paper, we introduce several methods to improve the accuracy of parameter evaluation in the measurement process by using linear (including an atomic/photon interferometer) and nonlinear interferometer to call quantum resources at different stages. High-precision measurement can be achieved by inputting non-classical states into the interferometer, such as compressed state, bi-fock state, and NOON state. And we also introduce the weak measurement developed for the direct observation of quantum states and its application to non-Hermitian systems, and the multiparameter measurement proposed to eliminate the accuracy balance between parameters. Compared with the first two measurement methods, weak measurement method is based on the weak value amplification principle of an indirect measurement. Measurements are performed virtually without perturbing the quantum system, which does not lead the wave function to collapse, the weak value of the real and virtual part have different physical significance, The combination of weak measurement theory and non-Hermitian system also further improves the measurement sensitivity. Multi-parameter measurement uses quantum entanglement, quantum control and other quantum resources to make the measurement progress reach the Heisenberg limit, which is the current research hotspot in the field of precision measurement. Furthermore, we present a conjecture whether there will be multi-atomic mixing measurements based on atomic spin effects or ultra-high sensitivity measurement instruments with precision of fT or even aT by using other particles detection. Finally, several measurement methods are analyzed and compared with each other, and the development prospect of quantum precision measurement is forecasted.