Enhancing parameter precision of optimal quantum estimation by quantum screening

We propose a scheme of quantum screening to enhance the parameter-estimation precision in open quantum systems by means of the dynamics of quantum Fisher information. The principle of quantum screening is based on an auxiliary system to inhibit the decoherence processes and erase the excited state to the ground state. By comparing the case without quantum screening, the results show that the dynamics of quantum Fisher information with quantum screening has a larger value during the evolution processes.

Modulating quantum Fisher information of qubit in dissipative cavity by coupling strength

By using the non-Markovian master equation, we investigate the effect of the cavity and the environment on the quantum Fisher information（QFI） of an atom qubit system in a dissipation cavity. We obtain the formulae of QFI for two different initial states and analyze the effect of the atom–cavity coupling and the cavity–reservoir coupling on the QFI.The results show that the dynamic behavior of the QFI is obviously dependent on the initial atomic states, the atom–cavity coupling, and the cavity–reservoir coupling. The stronger the atom–cavity coupling, the quicker the QFI oscillates, and the slower the QFI decreases. In particular, the QFI will tend to be a stable value rather than zero if the atom–cavity coupling is large enough. On the other hand, the smaller the cavity–reservoir coupling, the stronger the non-Markovian effect, and the slower the QFI decays. In other words, choosing the best parameter can improve the accuracy of the parameter estimation.In addition, the physical explanation of the dynamic behavior of the QFI is given by means of the QFI flow.

Dynamics of quantum Fisher information in a two-level system coupled to multiple bosonic reservoirs

We consider the optimal parameter estimation for a two-level system coupled to multiple bosonic reservoirs. By using quantum Fisher information （QFI）, we investigate the effect of the Markovian reservoirs＇ number N on QFI in both weak and strong coupling regimes for a two-level system surrounded by N zero-temperature reservoirs of field modes initially in the vacua. The results show that the dynamics of QFI non-monotonically decays to zero with revival oscillations at some time in the weak coupling regime depending on the reservoirs＇ parameters. Furthermore, we also present the relations between the QFI flow, the flows of energy and information, and the sign of the decay rate to gain insight into the physical processes characterizing the dynamics.

Optimal parameter estimation of open quantum systems

In quantum information technologies,quantum weak measurement is beneficial for protecting coherence of systems.In order to further improve the protection effect of quantum weak measurement on coherence,we propose an optimization scheme of quantum Fisher information(QFI)protection in an open quantum system by combing no-knowledge quantum feedback control with quantum weak measurement.On the basis of solving the dynamic equations of a stochastic two-level quantum system under feedback control,we compare the effects of different feedback Hamiltonians on QFI and find that via no-knowledge quantum feedback,the observation operatorσx(orσx andσz)can protect QFI for a long time.Namely,no-knowledge quantum feedback can improve the estimation precision of feedback coefficient as well as that of detection coefficient.

Environmental parameter estimation with the two-level atom probes

A novel scheme is proposed to estimate three environmental parameters,the detuning,the temperature and the squeezing strength with one-qubit or two-qubit probes.Quantum Fisher information and the fidelity of the atom probes are calculated.When the detuning between the frequency of cavity field and the atomic transition frequency is estimated,the dynamics of quantum Fisher information shows oscillatory and rising behaviors.To estimate the temperature of the thermal reservoir,the one-qubit probe with the superposition initial state is more favorable than the two-qubit probe with the entangled initial state.When the squeezing strength of the squeezed vacuum reservoir is estimated,we find that the estimation precision is significantly improved by utilizing the two-qubit probe with the maximal entangled initial state.Our work provides a potential application in the open quantum system and quantum information processing.

Optimal initial states for quantum parameter estimation based on Jaynes–Cummings model[Invited]

Quantum parameter estimation is a crucial tool for inferring unknown parameters in physical models from experimental data.The Jaynes–Cummings model is a widely used model in quantum optics that describes the interaction between an atom and a single-mode quantum optical field.In this Letter,we systematically investigate the problem of estimating the atom-light coupling strength in this model and optimize the initial state in the full Hilbert space.We compare the precision limits achievable for different optical field quantum states,including coherent states,amplitude-and phase-squeezed states,and provide experimental suggestions with an easily prepared substitute for the optimal state.Our results provide valuable insights into optimizing quantum parameter estimation in the Jaynes–Cummings model and can have practical implications for quantum metrology with hybrid quantum systems.

Parameter estimation in n-dimensional massless scalar field

Quantum Fisher information(QFI)associated with local metrology has been used to parameter estimation in open quantum systems.In this work,we calculated the QFI for a moving Unruh-DeWitt detector coupled with massless scalar fields in n-dimensional spacetime,and analyzed the behavior of QFI with various parameters,such as the dimension of spacetime,evolution time,and Unruh temperature.We discovered that the QFI of state parameter decreases monotonically from 1 to 0 over time.Additionally,we noted that the QFI for small evolution times is several orders of magnitude higher than the QFI for long evolution times.We also found that the value of QFI decreases at first and then stabilizes as the Unruh temperature increases.It was observed that the QFI depends on initial state parameterθ,and Fθis the maximum forθ=0 orθ=π,Fφis the maximum forθ=π/2.We also obtain that the maximum value of QFI for state parameters varies for different spacetime dimensions with the same evolution time.

Multi-objective optimization in quantum parameter estimation

We investigate quantum parameter estimation based on linear and Kerr-type nonlinear controls in an open quantum system, and consider the dissipation rate as an unknown parameter. We show that while the precision of parameter estimation is improved,it usually introduces a significant deformation to the system state. Moreover, we propose a multi-objective model to optimize the two conflicting objectives:(1) maximizing the Fisher information, improving the parameter estimation precision, and(2)minimizing the deformation of the system state, which maintains its fidelity. Finally, simulations of a simplified ε-constrained model demonstrate the feasibility of the Hamiltonian control in improving the precision of the quantum parameter estimation.

Quantum Fisher Information of Driven Multi-particle Systems in Structured Bosonic Reservoirs

We investigate the dynamics of the precision of the parameter estimation in many driven atoms, each of which interacts with a local structured bosonic reservoir respectively. The evolution of quantum states for single driven atom is described by the time local quantum master equation. The dynamics of the quantum Fisher information for many entangled atoms is obtained by means of the supreoperator mapping. The estimation limit is superior to the standard quantum limit during a characteristic interval. At a given time, the precision of parameter estimation can be improved to a maximal value if the number of entangled atoms is chosen to be an optimal value. The optimal number of entangled atoms is determined by the dynamical property. The decay of quantum Fisher information is accelerated with the increase of the number of entangled atoms.

Holevo bound independent of weight matrices for estimating two parameters of a qubit

Holevo bound plays an important role in quantum metrology as it sets the ultimate limit for multi-parameter estimations,which can be asymptotically achieved.Except for some trivial cases,the Holevo bound is implicitly defined and formulated with the help of weight matrices.Here we report the first instance of an intrinsic Holevo bound,namely,without any reference to weight matrices,in a nontrivial case.Specifically,we prove that the Holevo bound for estimating two parameters of a qubit is equivalent to the joint constraint imposed by two quantum Cramér–Rao bounds corresponding to symmetric and right logarithmic derivatives.This weightless form of Holevo bound enables us to determine the precise range of independent entries of the mean-square error matrix,i.e.,two variances and one covariance that quantify the precisions of the estimation,as illustrated by different estimation models.Our result sheds some new light on the relations between the Holevo bound and quantum Cramer–Rao bounds.Possible generalizations are discussed.

Enhancing the precision of phase estimation by weak measurement and quantum measurement reversal

The enhancement of the precision of phase estimation in quantum metrology is investigated by employing weak measurement （WM） and quantum measurement reversal （QMR）. We derive the exact expressions of the optimal quantum Fisher information （QFI） and success probability of phase estimation for an exactly solving model consisting of a qubit interacting with a structured reservoir. We show that the QFI can be obviously enhanced by means of the WM and QMR in different regimes. In addition, we also show that the magnitude of the decoherence involved in the WM and QMR can be a general complex number, which extends the applicable scope of the WM and QMR approach.

运动参考系中量子Fisher信息

量子参数估计中的基本理论--量子Cramér-Rao不等式指出,参数估计的方差由量子Fisher信息的倒数决定,量子Fisher信息越大,参数估计的方差就越小,估计精度也就会越高.在非相对论量子力学中,量子Fisher信息已被广泛研究,但考虑相对论效应对量子Fisher信息影响的研究相对较少.本文采用粒子态的相对论变换方法,数值计算和分析了运动参考系中单粒子态、双粒子态振幅参数θ和相位参数φ的量子Fisher信息.结果表明,在运动参考系中,无论是使用单粒子态还是双粒子态,量子Fisher信息都会降低.对于相位参数,双粒子态的量子Fisher信息比单粒子态降低得更加显著.然而,对于振幅参数,双粒子态的量子Fisher信息相对于单粒子态有所提高,该研究结果为在相对论效应的影响下提高参数估计精度提供了有价值的参考.

Quantum metrology with a non-Markovian qubit system

The dynamics of the quantum Fisher information(QFI) of phase parameter estimation in a non-Markovian dissipative qubit system is investigated within the structure of single and double Lorentzian spectra. We use the time-convolutionless method with fourth-order perturbation expansion to obtain the general forms of QFI for the qubit system in terms of a non-Markovian master equation. We find that the phase parameter estimation can be enhanced in our model within both single and double Lorentzian spectra. What is more, the detuning and spectral width are two significant factors affecting the enhancement of parameter-estimation precision.

非厄米哈密顿量中的量子Fisher信息与参数估计

量子Fisher信息给出参数估计的最优精度极限,在量子度量学中有重要的应用.近年来,在量子系统中实现非厄米哈密顿量的理论与实验研究受到广泛关注.本文研究基于非厄米哈密顿量本征态的参数估计,给出其中单参数与两参数估计的量子Fisher信息及其量子Cramér-Rao下界,计算与分析非互易、具有增益-耗散的Su-Schrieffer-Heeger模型,非厄米量子Ising链、拓扑陈绝缘体模型和二能级系统中动量及外场参数估计的量子Fisher信息.结果表明:在这几个非厄米模型中,对于单参数估计,量子Fisher信息在能隙闭合区域和例外点附近显著增大,从而提高参数估计的精度极限;对于两参数估计,量子Fisher信息矩阵的行列式在能隙闭合和例外点附近同样明显增大,拓扑区域比平庸区域的整体评估精度更高,且由陈数确定两参数估计误差的拓扑下界.

损耗SU(2)和SU(1,1)干涉仪中灵敏度过高估计的研究

基于损耗SU(2)和SU(1,1)干涉仪模型,以干涉仪中的相位估值的为研究方向,在理论上研究了与双参量相位估值相比,进行单参量相位估值的时候存在的高估量子Fisher信息(quantum Fisher information,QFI)的一般表达式;以相干态和压缩真空态输入为例,数值分析了高估QFI随损耗系数或分束比的变化,发现这时出现的高估QFI的消失和恢复现象是和分束比,增益因子以及压缩振幅具有一定的关系.通过调整分束比和损耗系数,可获得最佳的灵敏度,有利于在有损环境下进行量子精密测量.

基于Jaynes-Cummings模型的量子参数估计与初态优化

参数估计理论是根据实验测量数据推断物理模型中未知参数的重要理论工具.Jaynes-Cumming模型是量子光学中广泛使用的模型,描述了二能级原子和单模量子光场之间的相互作用.利用参数估计理论系统地研究了该模型中光-原子耦合强度g的估计精度,并找到了可达到最高估计精度的初态.该结果可以提高基于Jaynes-Cumming模型的量子精密测量的精度,该研究方法也可用于其他基于混合量子系统的量子度量学研究.

量子退相位通道中量子Fisher信息动力学

利用量子通道估计方法研究了纯退相位通道下,2个相互作用量子比特系统退相干率的量子Fisher信息的动力学演化。数值计算表明:量子Fisher信息总是先从0增加到某一最大值后迅速衰减,最后又减小到0;退相干率越大,导致量子Fisher信息越小和衰减到0的时间也越短;提高初始输入态的纠缠不能使最大量子Fisher信息得到提升。

Phase estimation of phase shifts in two arms for an SU(1,1)interferometer with coherent and squeezed vacuum states

We theoretically study the quantum Fisher information（QFI） of the SU（1,1） interferometer with phase shifts in two arms by coherent squeezed vacuum state input, and give the comparison with the result of phase shift only in one arm.Different from the traditional Mach–Zehnder interferometer, the QFI of single-arm case for an SU（1,1） interferometer can be slightly higher or lower than that of two-arm case, which depends on the intensities of the two arms of the interferometer.For coherent squeezed vacuum state input with a fixed mean photon number, the optimal sensitivity is achieved with a squeezed vacuum input in one mode and the vacuum input in the other.

双数态输入型M-Z干涉仪中量子相位的最大似然估计和贝叶斯分析

本文采用最大似然估计和贝叶斯分析两种方法,对双数态输入型马赫-曾德尔干涉仪中的量子相位估计进行研究.通过对干涉仪输出端粒子数差和宇称进行理论计算和数值模拟,发现采用贝叶斯分析和粒子数差测量的组合,可以在全相位空间实现最优测量,即待估相位精度达到由量子克拉美罗下界所给定的测量极限,同时,利用贝叶斯分析进行相位估计所需样本数较最大似然估计更少.在通过宇称测量进行相位估计的研究中,发现无法利用贝叶斯分析实现相位估计,但可采用最大似然估计进行研究.借助蒙特卡洛数值模拟分析,我们验证了理论计算结果,即相位估计精度会随待估相位θ0的变化而改变,将其与粒子数差测量结果对比,进一步确认了粒子数差测量方案的优越性.

基于量子Fisher信息的耗散相互作用光-物质耦合常数的估计

量子参数估计在量子度量学中有着重要的应用,量子Cramer-Rao下界表明量子参数估计精度极限与量子Fisher信息是直接相关的.本文利用量子参数估计理论对光场与原子失谐很大(大失谐)的Jaynes-Cummings模型耦合常数进行估计.制备探测初态为Qubit系统与光场的直积态,光场分别为Fock态、热态和相干态,分别计算了这三种探测态经大失谐Jaynes-Cummings模型哈密顿量演化后复合系统以及Qubit和光场系统的量子Fisher信息.通过分析发现,复合系统的量子Fisher信息随平均光子数单调递增,Qubit基态与激发态的等权叠加态为最优探测态,此时量子Fisher信息达到最大值;当探测态的光场为Fock态和热态时,关于被估计参数的信息都包含于Qubit系统;对于大失谐Jaynes-Cummings模型耦合常数的估计,光场为热态或相干态时耦合常数的估计精度高于光场为Fock态时的精度.