Discontinuity and Protection of Quantum Fisher Information for a Two-Qubit System

We analytically investigate the dynamics of quantum Fisher information of two qubits in independent environments for both uncorrelated and entangled input states.Especially,we observe that,in the non-Markovian regime and resonant case,quantum Fisher information of uncorrelated input state vanishes only at discrete time point whereas that of entangled input state can disappear during finite time interval.It shows that quantum Fisher information,which determines the parameter estimation precision,is strongly affected by the environment memory effects,and the advantage of entanglement-enhance metrology no longer exists even for a very short time.We also note that quantum Fisher information for two kinds of input states can be preserved under appropriate qubit-reservoir detuning.     

Discontinuity and Protection of Quantum Fisher Information for a Two-Qubit System

We analytically investigate the dynamics of quantum Fisher information of two qubits in independent environments for both uncorrelated and entangled input states. Especially, we observe that, in the non-Markovian regime and resonant case, quantum Fisher information of uncorrelated input state vanishes only at discrete time point whereas that of entangled input state can disappear during finite time interval. It shows that quantum Fisher information, which determines the parameter estimation precision, is strongly affected by the environment memory effects, and the advantage of entanglement-enhance metrology no longer exists even for a very short time. We also note that quantum Fisher information for two kinds of input states can be preserved under appropriate qubit-reservoir detuning.     

Estimation of the disorder degree of the classical static noise using three entangled qubits as quantum probes

The paper investigates the estimation of the disorder degree of the classical static noise using three entangled qubits as quantum probes together with the tools of local quantum estimation theory. Three probing schemes namely common environment (CE), independent environments (IEs) and mixed environments (MEs) are investigated and the optimal initial state preparation of the probes taken as a partially depolarized GHZ state. The results show that: (i) the IEs probing scheme allows one to achieve better estimation precision compared to both MEs and CE schemes respectively; (ii) the higher is the initial amount of entanglement of the probes, the larger is the estimation precision, independently of the scheme considered; (iii) both small and large values of the disorder parameter are uniformly estimable at the optimal interaction time; (iv) entangled qubits probes quickly encode information about the disorder parameter than single-qubit probe; (v) there is an improvement in the estimation of the disorder parameter when entangled probes interacting either in IEs or MEs are used instead of a single probe, demonstrating that a single probe is not sufficient to optimally estimate the disorder parameter of the static noise. On the other hand, we have also investigated the relationship between the residual amount of entanglement present in the probes at the optimal interaction time and the estimation precision of the disorder parameter. We show that the higher the residual amount of entanglement at the optimal interaction time, the smaller the estimation precision.     

Enhancing the Precision of Parameter Estimation in Band Gap

Recently, the dynamics of quantum Fisher information(QFI) in various environment are investigated and many kinds of schemes to overcome the drawback of decoherence are designed. Here we propose the pseudomode method to enhance the phase parameter precision of optimal quantum estimation of a qubit coupled to a non-Markovian structured environment. We find that the QFI can be enhanced in the weak-coupling regime with non-perfect band gap and can be trapped permanently with a large value in the perfect band gap. The effects of qubit-pseudomode detuning and the spectrum of reservoir are discussed, a reasonable physical explanation is given, too.     

Improving Quantum Metrology via Purifying and Distilling Noisy Probe States

In quantum metrology, the precision of unknown parameter estimation is studied in the quantum regime, and the choice of the probe state plays an important role in determining the precision of the parameter to be estimated. The quality of quantum metrology will be reduced in the presence of quantum noise during the memory time of probe states after preparation. Meanwhile the noisy probe state can be manipulated by different protocols such as single‐qubit purification, entanglement purification, and entanglement distillation etc. In this paper, the effects of these manipulations on the usefulness, that is, quantum Fisher information (QFI), of the noisy probe state in quantum metrology are studied. The results show that joint operations in single‐qubit purification and entanglement purification processes play positive roles in enhancing the QFI of the probe states, and local measurements in entanglement purification and entanglement distillation processes play both positive and negative roles in enhancing the QFI of the probe states. In this sense, single‐qubit purification will always be helpful in parameter estimation by using single qubits as probe, and entanglement purification process maybe more suitable for improving the estimation precision when entangled‐state probe is adopted.     

超冷原子系综的非高斯纠缠态与精密测量

量子精密测量是基于量子力学的基本原理对特定物理量实施测量,并利用量子效应提高测量精度的交叉科学.随着超冷原子实验技术的发展,超冷原子为量子精密测量提供了一个优异的研究平台.利用发展成熟的量子调控技术,人们可以基于超冷原子系综制备一些新奇的非高斯多粒子纠缠态.基于多体量子干涉,利用这些非高斯纠缠态作为输入,可以实现超越标准量子极限的高精度测量.本文简要综述这一研究领域的进展.     

一种基于von Neumann熵的双路径纠缠量子微波信号生成质量评估方法

针对目前没有合适的方法从产生方来表征纠缠量子微波信号的质量好坏, 提出了一种基于von Neumann熵的双路径纠缠量子微波信号生成质量评估方法. 利用双模压缩真空态描述了纠缠量子微波的信号格式, 给出了光子数与压缩参量之间的函数关系, 以熵评估纠缠态信号所占比例, 分析了熵与压缩参量和光子数之间的关系. 仿真结果表明, 纠缠量子微波信号中的光子数是由压缩参量决定的, 它们之间呈指数平方的规律性变化; 熵随着压缩参量的增大而减小, 但是减小的趋势越来越平缓, 近似呈负指数关系, 熵的极限值约为65%. 研究结果表明, 通过选择合适的压缩参量可以提高纠缠微波信号生成质量以满足实际需要, 因此, 本研究对于生成双路径纠缠量子微波电路参数选择、提高系统可用性提供了方法和依据.     

Optimal quantum parameter estimation of two-qutrit Heisenberg XY chain under decoherence

Adopting the Milburn decoherence model, we investigate the performance of quantum Fisher information of the twoqutrit isotropic Heisenberg XY chain under decoherence. We find that the quantum Fisher information with respect to the decoherence rate and the magnetic field decreases exponentially in the long-time limit, which significantly reduces the precision of optimal quantum estimation. We also show that with the increase of the decoherence rate or the magnetic field,the QFIs go down considerably. Furthermore, we find that the precision of optimal quantum estimation can be enhanced by the entanglement in the input state.     

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.     

Quantum parameter estimation in the Unruh–DeWitt detector model

Relativistic effects on the precision of quantum metrology for particle detectors, such as two-level atoms are studied. The quantum Fisher information is used to estimate the phase sensitivity of atoms in non-inertial motions or in gravitational fields. The Unruh–DeWitt model is applicable to the investigation of the dynamics of a uniformly accelerated atom weakly coupled to a massless scalar vacuum field. When a measuring device is in the same relativistic motion as the atom, the dynamical behavior of quantum Fisher information as a function of Rindler proper time is obtained. It is found out that monotonic decrease in phase sensitivity is characteristic of dynamics of relativistic quantum estimation. The origin of the decay of quantum Fisher information is the thermal bath that the accelerated detector finds itself in due to the Unruh effect. To improve relativistic quantum metrology, we reasonably take into account two reflecting plane boundaries perpendicular to each other. The presence of the reflecting boundary can shield the detector from the thermal bath in some sense.     

Modular-value-based metrology with spin coherent pointers

We discuss an optimal modular-value-based measurement with a spin coherent pointer: A quantum system is exposed to a field whose strength is to be estimated through its modular value. We evaluate the quantum Fisher information as a figure of merit. We found that the modular-value-based measurement can reach the same ultimate precision limit of the estimation as those of measurements without postselections. The quantum Fisher information can be increased when the dimension of the pointer state increases. We also consider the pointer under a phase-flip error. Our study should motivate researchers to apply the modular-value-based measurements for quantum metrology.     

Squeezed vacuum as a universal quantum probe

We address local quantum estimation of bilinear Hamiltonians probed by Gaussian states. We evaluate the relevant quantum Fisher information (QFI) and derive the ultimate bound on precision. Upon maximizing the QFI we found that single- and two-mode squeezed vacuum represent an optimal and universal class of probe states, achieving the so-called Heisenberg limit to precision in terms of the overall energy of the probe. We explicitly obtain the optimal observable based on the symmetric logarithmic derivative and also found that homodyne detection assisted by Bayesian analysis may achieve estimation of squeezing with near-optimal sensitivity in any working regime.     

Dynamics of Quantum Fisher Information in Two Component Bose-Einstein Condensate

We investigate quantum Fisher information dynamics in two component Bose-Einstein condensate interacting spins with an external field. Approximate analytical expressions of quantum Fisher information is presented. Our analysis shows that quantum Fisher information is controlled by adjusting the strength of the external field and the total atomic number. It is shown that the maximal mean quantum Fisher information is occurred and the phase estimation is enhanced to the Heisenberg limit under some conditions.     

Chaos and quantum Fisher information in the quantum kicked top

Quantum Fisher information is related to the problem of parameter estimation.Recently,a criterion has been proposed for entanglement in multipartite systems based on quantum Fisher information.This paper studies the behaviours of quantum Fisher information in the quantum kicked top model,whose classical correspondence can be chaotic.It finds that,first,detected by quantum Fisher information,the quantum kicked top is entangled whether the system is in chaotic or in regular case.Secondly,the quantum Fisher information is larger in chaotic case than that in regular case,which means,the system is more sensitive in the chaotic case.     

Estimation of the Parameters in a Two-State System Coupled to a Squeezed Bath

Estimation of the phase and weight parameters of a two-state system in a squeezed bath by calculating quantum Fisher information is investigated. The results show that, both for the phase estimation and for the weight estimation, the quantum Fisher information always decays with time and changes periodically with the phases. The estimation precision can be enhanced by choosing the proper values of the phases and the squeezing parameter. These results can be provided as an analysis reference for the practical application of the parameter estimation in a squeezed bath.     

Strong chaos of fast scrambling yields order: Emergence of decoupled quantum information capsules

The information loss problem in black hole evaporation is one of fundamental issues. Its resolution requires more profound understanding of information storage mechanism in quantum systems. In this Letter, we argue that when multiple unknown parameters are stored in large entangled qudits, strong chaos generated by fast scrambling in high temperature limit yields an ordered information storage structure with decoupled quantum information capsules (QICs). A rotational isometry emerges in the quantum Fisher information metric. The isometry is expected to be observed in future experiments on cold atoms in a pure entangled state. We provide a QIC speculation of black hole evaporation.     

Quantum Fisher Information and the Heisenberg Limit in Superpositions of Two W States and Symmetric State

We investigate the quantum Fisher information and the Heisenberg limit in superposition of a four-qubit symmetric state and two W states. Numerical and analytical calculations for quantum Fisher information and the Heisenberg limit of the four-qubit state are driven. It is shown that quantum Fisher information of the four-qubit state depends on the superposition coefficients and the relative phase. It is also shown that under certain conditions, the maximal quantum Fisher information occurred; which leads to the estimation sensitivity beats the Heisenberg limit.     

噪声对一种三粒子量子探针态的影响

量子度量学是研究量子测量与统计推断的一门学科,主要利用量子手段来提高参数估计的精度,在量子信息处理与测量中起到关键作用.量子参数估计的一般过程包含四个步骤:探针态的制备、参数化过程、对参数化后的输出态进行测量以及根据测量结果估计待测参数.其中探针态的选取对测量精度起着至关重要的作用.然而在实际的量子探针态的制备过程中,初始探针态会受到环境噪声的影响.目前人们已经研究了W态与Greenberger-Horne-Zeilinger(GHZ)态的量子Fisher信息(QFI)在典型噪声通道下的变化行为.由于W态与GHZ态有着不同的纠缠性质,对于W态与GHZ态的叠加态的QFI动力学研究具有重要的实际意义.故此,本文主要研究典型噪声通道对这两种状态的叠加态的QFI动力学行为的影响,得出了QFI随噪声参数的变化行为.结果表明,叠加态中W态组分可明显对抗相位阻尼噪声对探针态的QFI的影响,而其中的GHZ态组分可明显对抗振幅阻尼噪声的影响,从而为在实际环境中选取高精度的参数估计过程提供参考.     

Quantum Fisher Information and Heisenberg Limit in Multi-qubit State

We investigate the quantum Fisher information and Heisenberg limit in multi-qubit pure state superposed by a GHZ state and two W states with a relative phase. Analytical expressions of quantum Fisher information and phase estimation sensitivity are derived. It is shown that the maximal quantum Fisher information occurs and the phase estimation is enhanced to the Heisenberg limit when the number of qubits is large.     

Parameter estimation by decoherence in the double-slit experiment

We discuss a parameter estimation problem using quantum decoherence in the double-slit interferometer. We consider a particle coupled to a massive scalar field after the particle passing through the double slit and solve the dynamics non-perturbatively for the coupling by the WKB approximation. This allows us to analyze the estimation problem which cannot be treated by master equation used in the research of quantum probe. In this model, the scalar field reduces the interference fringes of the particle and the fringe pattern depends on the field mass and coupling. To evaluate the contrast and the estimation precision obtained from the pattern, we introduce the interferometric visibility and the Fisher information matrix of the field mass and coupling. For the fringe pattern observed on the distant screen, we derive a simple relation between the visibility and the Fisher matrix. Also, focusing on the estimation precision of the mass, we find that the Fisher information characterizes the wave-particle duality in the double-slit interferometer.