Multi-outcome Phase Measurement And Data Processing In A Quantum Interferometer

Quantum mechanics combines with statistical informatics to develop quantum metrology,which has potential applications in high-precision measurement,atomic clocks,gravitational wave detection and other fields.In recent years,precision measurement technology based on quantum interferometers has achieved rapid development,and measurement accuracy has been continuously improved.Quantum metrology is a discipline that aims at high-resolution and high-sensitivity measurement over physical parameters of quantum systems.Based on the two-mode quantum interferometer,starting from the general principle of quantum measurement,this paper studies the particle number difference measurement(i.e.,Jz measurement)and multi-outcome homodyne detection.Then analyzes the influence of these two measurement schemes on the output signal and phase sensitivity.Specifically,the following original research contents are as follows:1.Reconsidering the photon-number difference measurement scheme of the twinFock state interferometer,and analytically prove that the classical Fisher information of the photon-number difference measurement and the photon-number difference square measurement scheme are equal to each other and equal to the quantum Fisher information N(N+2)/2,which result is valid for any phase,and can achieve a global phase estimation accuracy(?).Besides,based on the 6-photon twin-Fock state experiment of Xiang et al.,we phenomenologically consider the imperfections of the experiment,numerically simulate the probability of all the measured values of the particle number difference measurement,and use the root mean square error between the maximum likelihood estimator and the true value Measure the accuracy of phase measurement.Our research results found that:(?)the measurement accuracy can break through the standard quantum limit and approach the Heisenberg limit;(?)the quantum gain sensing interval is twice as large as the previous projection measurement scheme;(?)under a finite number of measurements,the maximum likelihood estimator is unbiased,and can saturate the Cramer-Rao lower limit of the phase measurement accuracy.2.Based on the squeezed light interferometer,we study the output signal and phase sensitivity of multi-outcome homodyne detection.Our scheme avoids the divergence problem of phase sensitivity at ??0.In addition,our results can improve phase resolution and phase sensitivity at the same time,achieving so-called super-resolution and super-sensitivity.Besides,aiming at the multi-value output problem in phase estimation,we have developed a new phase estimator.Since the analytic expression of the estimator is a superposition of multiple inverse function estimators,it is called the linear combination of inverse function estimators,or linear combination estimators for short.Take the homodyne detection of a squeezed light interferometer as an example to numerically demonstrate the new data processing method.We found that when the number of measurements is large,the new estimator is progressively unbiased,and the sensitivity can fully saturate the Cramer-Rao lower bound.Provide a theoretical basis for the follow-up research on quantum measurement and quantum perception.In the first chapter of this paper,we introduce the background of quantum measurement,the general steps of quantum measurement and the knowledge of two mode quantum interferometer.In addition,we also introduce the research progress of quantum phase measurement and the basis of topic selection.The second chapter introduces the classical Fisher information,quantum Fisher information,inversion method and maximum likelihood estimation.Chapter third introduces the optimal phase estimation with photon-number difference measurement using twin-Fock states of light.Chapter fourth introduces single-port homodyne detection and data processing based on squeezed light interferometer.Finally,we summarize the full paper.