Research On Quantum Fisher Information And Phase Estimation Based On SU(1,1) Interferometer

Quantum metrology,also known as quantum precision measurement,is a discipline combining quantum mechanics and precision measurement.It aims to use the knowledge of quantum mechanics and parameter estimation to accurately measure physical quantities.At present,quantum metrology has been widely used in the measurement of gravitational waves,electric fields,weak magnetic fields,and atomic frequencies.The basic theory of quantum metrology-the quantum Cramér-Rao theorem,stipulates that the theoretical maximum parameter estimation accuracy is determined by the inverse of the quantum Fisher information,so the solution of quantum Fisher information is important in this field.However,in the actual parameter estimation scheme,when we estimate an unknown physical quantity,the maximum accuracy limit that can be achieved in practice is the standard quantum limit.In order to obtain higher estimation accuracy,the maximum accuracy limit that can be achieved by using a quantum scheme is the Heisenberg limit.Optical interferometer is an important tool to study quantum metrology.This paper is based on the nonlinear SU(1,1)interferometer with the coherent state and the squeezed vacuum state as input.The main work is to analyze the phase sensitivity that can be obtained under different phase shift modes(one-and two-arms).First,we calculate the quantum fisher information with two phase shifts and compare the theoretical accuracy separately.It shows that the two-arm phase shift mode performs a better accuracy when the strength of squeezed state is large enough.Furthermore,this article uses homodyne detection to study the achievable accuracy and find that both two phase shift modes have the same measurement accuracy at the optimal point.And they can both break through the standard quantum limit and reach the Heisenberg limit,but fail to reach their respective theoretical accuracy limits,indicating that homodyne detection is a suboptimal detection scheme at this time.In addition,we also simulated the internal noise and external noise of the interferometer caused by the photon loss in the actual environment.The study found that the internal noise has a greater impact on the actual detection accuracy than the external noise.Further,we propose an unbalanced SU(1,1)interferometer that can well solve the impact of detection noise on measurement accuracy.