Quantum Fisher Information Research In Open Quantum Systems

In recent years,the rapid development of quantum metrology has attracted a lot of at-tention.Its core issue is on the precision of measurement.The maximal acquirable precision of quantum measurement depends on quantum Fisher information(QFI).And QFI depend-s crucially on quantum entanglement and coherence,but in open quantum system,system will inevitably interact with its surrounding environment,which will hinder acquiring high precision in quantum parameter estimation.In this thesis,we mainly investigate the QFI dynamics of N-qubit GHZ state driven by phase noise lasers(PNL),and QFI dynamics of N-qubit GHZ state under weak measurement with pre-and post-flips against amplitude damping channel(ADC).And by numerical calculation we display the character of QFI of t-wo qubit entangled state which is driven by random telegraph noise(RTN)with dipole-dipole interaction,or driven by PNL with dipole-dipole interaction and collective decay.And we try to find the protecting method against these noises in open quantum system according to the QFI dynamic characteristics.The entire thesis consists of the following five parts.In the first chapter,we introduce the history of the quantum metrology,and the signif-icance of the QFI.In the second chapter,we introduce the basic fundamental knowledge of QFI,the inequality of the Cram?er-Rao,the dissipation channel and the basic theory of the quantum measurement.In the third chapter,the dynamics of N-qubit GHZ state QFI under PNLs driving is in-vestigated in terms of non-Markovian master equation.We first investigate the non-Markovian dynamics of QFI for N-qubit GHZ state and show that when the ratio of the PNL rate and the system-environment coupling strength is very low,the oscillations of the QFIs decay s-lower which corresponds to the non-Markovian region;but when it becomes large,the QFIs monotonously decay which corresponds to the Markovian region;when it becomes very large the QFIs even hold on or only slightly decay.And when the atom number N increases,QFIs in both regions decay faster.We further find that the QFI flow disappears suddenly followed by a sudden recovery depending on the ratio of the PNL rate and the system-environment coupling strength and the atom number N,which unveils a fundamental connection between the non-Markovian behaviors and the parameters of system-environment couplings.We dis-cuss two optimal positive operator-valued measures(POVMs)for two different strategies of our model and find the condition of the optimal measurement.Under this condition,it is feasible to get the QFI which means the precision can reach Heisenberg limit.In the fourth chapter,by using weak-measurement-based pre-and post-flips(WMPPF),we propose a scheme to protect the average QFI in the independent ADC for N-qubit GHZ state and the generalized N-qubit GHZ states.We also discuss the weak measurement and quantum measurement reversal(WMQMR)for the same ADC.Based on the analytical and numerical results we obtain the main result:the WMPPF can reduce the effect of dissipation on the average QFI of the phase or the frequency for GHZ state and some generalized GHZ states,and the WMQMR can reduce the effect of dissipation on the average fidelity for GHZ state and generalized GHZ states in ADC.Comparing QFI with fidelity for WMPPF or for WMQMR,a scheme protecting the average fidelity does not necessarily protect the average QFI,even with the same parameters,and vice versa.We also focus on the average QFI varying with the qubit number N in the phase estimation and the frequency estimation of WMPPF,both of which show that the advantages over the do-nothing(DN)case.And we also obtain the optimal N in our WMPPF scheme for these two estimations.In the last chapter,firstly,we numerically calculate the QFI of two atoms with qubit-qubit interaction under RTNs.The result shows the qubit-qubit interaction is helpful for protecting the QFI.We find that the system under the RTN has similar dynamic characteris-tics with PNL model,and we can use the non-Markovian dynamics to get high QFI at some special times.And in the Markovian region,we can also use large rate between switching frequency and coupling coefficient to protect the QFI.Secondly,we investigate the param-eter estimation problem of two-atom system driven by the PNL.Under the consideration of atom system without dipole-dipole interaction and without the dissipation,we compare the numerical calculation result with the analysis result in the former chapter(i.e.,chapter three)on QFI,and find that the former is consistent with the latter.Thirdly,we consider the dipole-dipole interaction between the atoms and the collective decay^[1,2].And the result shows that the smaller collective decay rate leads to larger QFI of the two-atom system.So we can conclude that collective decay will destroy the QFI while the dipole-dipole interaction will protect the QFI.This conclusion can be used in the open systems,and when there are phase diffusion and dissipation,it can protect the QFI.And this is one of the main conclusions of this chapter.