On The Weak-value Measurement Of Quantum Systems And Its Application

Nowadays,most researchers choose the projective measurement to acquire the information of quantum systems,whose results are definitely within the eigenvalue spectrum of the measurement operator,however there is a so called weak-value measurement method,whose results can be outside of the eigenvalue spectrum.First proposed in 1988,the quantum weak-value measurement has become an experimental tool with functions of amplifying small signals,obtaining complex-number-valued observable results and measuring nonclassical features in quantum systems.The definition of a weak-value,the physical interpretation,the procedure of weak-value measurement and related applications are extensively studied,however it seems that researchers have not reached a consensus on the physical interpretation of a weak-value.In this dissertation according to the mathematical expression,the weak-value is regarded from a practical view as a conditioned observable expectation related to the measurement operational procedure.Some theoretical and applicative problems are discussed on the weak-value measurement at quantum systems in this dissertation,whose main contents and innovations are as follows:(1)Improving the physical realization of an optical-field quantum state tomography scheme under weak-value measurement through the polarization intensity.In some present schemes of optical-field quantum state tomography via weak-value measurement,the homodyne detection is employed to perform both the post-selection and the probebeam-information readout recording.However,it requires an extreme accurate localoscillator phase modulation,which is a demanding requirement on the operational technique of experimentalists.To overcome this defect,an optical-field quantum state tomography scheme via weak-value measurement with an improved physical realization is proposed,in which the quadrature of the optical mode is represented with the optical-field polarization intensity and the target quantum state is reconstructed from the weak-values calculated from measured polarization intensities.The principle of this improved scheme is analyzed and numerically simulated,and the difference between the improved scheme and the original one in the process of quantum state tomography is demonstrated to reveal the advantage of our scheme.In addition,some constructive suggestions about this new scheme are presented,based on the analyses of parameter sensitivity and scheme's robustness,including the validating condition and the influence on the tomography result from the experimental parameter setting as well as from particular experimental errors.(2)Proposing an optical-field quantum state tomography scheme outside the weakinteraction regime under the all-order model of the weak-value measurement.Generally,working within the weak-interaction regime is a precondition for the weak-value measurement schemes,and the first-order approximate model is an effective tool to analyze these schemes,however when the precondition is not satisfied,such model will augment the system-inherent difference.To overcome this disadvantage of the applicative precondition for the weak-value measurement and according to the mechanism modeling method in the control discipline,a new model with an all-order expansion of the Taylor series on the unitary evolution operator is considered to describe the weak-value measurement process where the weak-interaction regime is exceeded,and the feasibility of this new model is verified through a particular experiment scheme.This scheme is for quantum state tomography over the planar laser-energy distribution via weak-value measurement with combination of the compressive sensing technique,and its implementation procedure contains a parameter self-adaptive adjustment.The numerical simulation shows that this new model could improve the fidelity of the quantum state tomography.It is also revealed through the parameter sensitivity analysis that the upper boundary of the weak-interaction regime permitted by the first-order approximate model in the original scheme is 1/5 of the coupling-strength maximum,and the same boundaries for higher-order approximate models are shown to get larger with the increase of the model order,furthermore the upper boundary for the all-order model is the maximum of the coupling strength.(3)Analyzing the experimental error influence on the optical-field quantum state tomography via weak-value measurement.It is impossible that the practical process of the weak-value measurement is not disturbed by any experimental error.Through introducing the robustness analysis method in the control discipline,we explore the influence of the detector's measurement-basis-deflecting error on the result of the quantum state tomography in the last step of the weak-value measurement procedure,and quantify the influence on tomography with two equivalent indices—the fidelity and the trace distance between the tomography result and the true state.The mathematical expression of the quantum state tomography result with fidelity and trace distance are obtained through considering the error disturbance.Toward particularly-formulated quantum states,we find out a robust state pattern insensitive to such error through numerical simulation,i.e.quantum states with near 50% vector elements carrying phase ?.Notice that the states within this pattern are suitable candidates for the task of quantum information transferring.Moreover,the difference between the error-disturbance sensitivity for the weak-value measurement and that for the projective measurement is examined and the reason is analyzed.(4)Providing an optical-field quantum state discrimination scheme via weak-value measurement.Toward the quantum state discrimination where the projective measurement is not applicable,the feasibility of using the weak-value measurement is explored.We first propose an optical-field quantum state discrimination scheme via parameteroptimized weak-value measurement on particular planar laser-energy distributions,and analyze the role of the weak-value measurement in the process of the quantum state discrimination as well as that in the quantum state tomography.It is found through comparative analysis and numerical simulation that the cost in quantum state discrimination is lower than in quantum state tomography.This is because their differences in the task goal and available a priori information lead to different performing numbers of times for the weak-value measurement procedure.Meanwhile,through the parameter sensitivity analysis,we reveal the relation among the sampling quantity of experiment data,the precision of the weak-value measurement and the confidence level,and present the related mathematical expression and some numerically simulated examples.