The Optimal Measurement For Estimating A Coupling Strength In Quantum Measurement

In this thesis,we try to find out the optimal measurement for estimating a coupling strength.For this intention,we figure out the strict expression of the measurement outcome after the postselection,and derive the max value of the measurement outcome.Especially,we compare the performance of the estimations via measuring the position and measuring the momentum of the pointer of the measurement device,with and without postselection.Without postselection,it turns out that all the information about the coupling strength can be extracted by measuring the position of the pointer.As a contrast,there would be no information if the momentum is measured without postselection.Hence if postselection is not allowed,measuring the position is the better choice.When postselection is employed,we find that no matter which observable among the position and the momentum is measured,postselection,when it is partially optimized,provides a great amplification of the measurement outcome,which can be larger than the initial standard deviation of the pointer under certain circumstances,at an acceptable cost of losing a little accuracy of the estimation of the coupling strength.Finally,it is considered that the variance of coupling strength is inversely proportional to the weak value of the mechanical quantities of the system when the instrumental state is a qubit state and postselection is employed.