Fisher information due to a phase noisy laser under non-Markovian environment

More recently, K. Berrada [Annals of Physics 340 (2014) 60-69] [1] studied the geometric phase of a two-level atom system driven by a phase noise laser under non-Markovian dynamics in terms of different parameters involved in the whole system, and collapse and revival phenomena were found for large class of states. In this paper, using this noise effect, we study the quantum fisher information (QFI) for a two-level atom system driven by a phase noise laser under non-Markovian dynamics. A new quantity, called QFI flow is used to characterize the damping effect and unveil a fundamental connection between non-Markovian behavior and dynamics of system–environment correlations under phase noise laser. It is shown that QFI flow has disappeared suddenly followed by a sudden birth depending on the kind of the environment damping. QFI flow provides an indicator to characterize the dissipative quantum system’s decoherence by analyzing the behavior of the dynamical non-Markovian coefficients.     

多粒子GHZ纠缠实验中Fisher信息的保真度方法获取

保真度与Fisher信息在量子精密测量和量子纠缠判定中充当着非常重要的角色。本文从概率统计和量子力学的角度出发,阐明了两者之间的区别与联系,给出了保真度方法获取Fisher信息的数学表达式;基于量子测量中常见的宇称测量模型,我们对多粒子Greenberger-Horne-Zeilinger (GHZ)纠缠产生实验中Fisher信息的获取开展了保真度方法研究,通过对实验数据的蒙特卡洛模拟,二阶或高阶曲线拟合获取了系统的Fisher信息,并将其与理论计算结果进行对比,结果表明保真度方法可以有效地获取量子系统的Fisher信息,当体系粒子数目较少时,宜采用二阶拟合方法获取系统的Fisher信息,而当粒子数目较多时,需考虑高阶拟合项的影响。此外,我们还将多光子GHZ纠缠实验中Fisher信息的保真度获取结果与海林格距离方法的获取结果进行对比,发现二者是一致的,这也进一步验证了保真度方法获取Fisher信息的有效性。本文的研究也为开展与Fisher信息相关的量子拓扑学和量子相变的研究提供了新的途径。     

Improving the teleportation of quantum Fisher information under non-Markovian environment

Quantum teleportation is designed to send an unknown quantum state between two parties. In the perspective of remote quantum metrology, one may be interested in teleporting the information that is encoded by physical parameters synthesized by quantum Fisher information (QFI). However, the teleported QFI is often destroyed by the unavoidable interaction between the system and the environment. Here, we propose two schemes to improve the teleportation of QFI in the non-Markovian environment. One is to control the quantum system through the operations of weak measurement (WM) and corresponding quantum measurement reversal (QMR). The other is to modify the quantum system based on the monitoring result of the environment (i.e., environment-assisted measurement, EAM). It is found that, in the non-Markovian environment, these two schemes can improve the teleportation of QFI. By selecting the appropriate strengths of WM and QMR, the environment noise can be completely eliminated and the initial QFI is perfectly teleported. A comprehensive comparison shows that the second scheme not only has a higher probability of success than the first one, but also has a significant improvement of the teleported QFI.     

Geometric phase of a qubit driven by a phase noise laser under non-Markovian dynamics

Robustness of the geometric phase (GP) with respect to the environmental effects is a basic condition for an effective quantum computation. Here, we study quantitatively the GP of a two-level atom system driven by a phase noise laser under non-Markovian dynamics in terms of different parameters involved in the whole system. We find that with the change of the damping coupling, the GP is very sensitive to its properties exhibiting long collapse and revival phenomena, which play a significant role in enhancing the stabilization and control of the system dynamics. Moreover, we show that the GP can be considered as a tool for testing and characterizing the nature of the qubit–environment coupling. Due to the significance of how a system is quantum correlated with its environment in the construction of a scalable quantum computer, the entanglement dynamics between the qubit with its environment under external classical noise is evaluated and investigated during the time evolution.     

Two schemes of teleportation one-particle state by a three-particle GHZ state

In accordance with transformation operator, we give two schemes for teleporting an unknown one-particle state via a general GHZ state, Two Von Neumann type measurements are given for teleporting an unknown one-particle state. The first Von Neumann type measurement use four orthogonal states and the second Von Neumann type measurement is eight orthogonal states. For maximally entangled GHZ state, the successful probability and fidelity of two schemes both reach 1.     

Precision of estimation and entropy as witnesses of non-Markovianity in the presence of random classical noises

We investigate in detail the quantum Fisher information (QFI) behavior by examining a single qubit model in the presence of random classical noises in both Markovian and non-Markovian regimes. In particular, we precisely study the effects of noise switching rate ξ$\xi$ and qubit–environment coupling strength ν$\nu$ on the precision of estimation, when the qubit is subjected to random telegraph noise with a Lorentzian spectrum or colored noise with a spectrum of the form 1/f^α$1/f^{\alpha }$. In the Markovian regime, a monotone decay of the QFI with time is found, whereas for non-Markovian noise sudden death and revivals may occur. Despite these oscillations of the QFI in non-Markovian regime, we find that non-Markovian parameter γ=ξ/ν$\gamma =\xi /\nu$ is not the principal parameter controlling the collapse and revival of the QFI. In fact, in both Markovian and non-Markovian regimes, parameters ξ$\xi$ and ν$\nu$independently determine how the QFI varies. We also find that the QFI in the case of colored environments decreases when the number of fluctuators realizing the noise increases, and therefore the parameter estimation becomes more inaccurate. Furthermore, by analyzing the von Neumann entropy of the system density matrix, we illustratively unveil a fundamental relationship between the dynamics of this quantity and non-Markovian behavior in the presence of random classical noises. We also show that this result may lead to a better non-Markovianity interpretation, based on quantum memory effects. Moreover, we demonstrate the connection between the precision of parameter estimation and rising the non-Markovianity in our model where the environment is modeled as classical.     

Fisher information description of the classical-quantal transition

We investigate the classical limit of the dynamics of a semiclassical system that represents the interaction between matter and a given field. The concept of Fisher Information measure (F) on using as a quantifier of the process, we find that it adequately describes the transition, detecting the most salient details of the changeover. Used in conjunction with other possible information quantifiers, such as the Normalized Shannon Entropy (H) and the Statistical Complexity (C) by recourse to appropriate planar representations like the Fisher Entropy (F×H) and Fisher Complexity (F×C) planes, one obtains a better visualization of the transition than that provided by just one quantifier by itself. In the evaluation of these Information Theory quantifiers, we used the Bandt and Pompe methodology for the obtention of the corresponding probability distribution.     

Fisher information,Rényi entropy power and quantum phase transition in the Dicke model

Fisher information, Rényi entropy power and Fisher–Rényi information product are presented for the Dicke model. There is a quantum phase transition in this quantum optical model. It is pointed out that there is an abrupt change in the Fisher information, Rényi entropy power, the Fisher, Shannon and Rényi lengths at the transition point. It is found that these quantities diverge as the characteristic length: |_λc−λ|^−1/4${|{\lambda }_c-\lambda |}^{-1/4}$ around the critical value of the coupling strength _λc${\lambda }_c$ for any value of the parameter β$\beta$.     

Geometric phase,entanglement, and quantum Fisher information near the saturation point

Considering a collection of two-level atoms in the presence of a saturating monochromatic, steady-state field, we investigate the geometric phase (GP) of an arbitrary medium’s atom. We find that it is possible to detect the saturation of the atomic response by the GP computation. This is an interesting result, because we can predict the collective behaviour of the atomic system—i.e., the saturation of the optical response of the medium- by investigating the GP of a single medium’s atom, described as a qubit. Moreover, we find that the plot of the atomic GP in terms of the detuning Δ$\Delta$ is very similar to the absorption spectrum of the medium. In addition, it is shown that when the intensity of the driving laser field tends to saturation intensity, the qubit approaches maximum correlation with its environment described by the driving field and other qubits in the atomic system. Furthermore, we find that the behaviour of the entanglement is very analogous to that of the GP and the absorption coefficient. Besides, we adopt the atom to estimate the decoherence parameter by using the quantum Fisher information (QFI), an important measure of the information content of quantum states. Interestingly, we find that when the atomic system approaches its saturation point, the QFI decays with increasing the laser intensity, and therefore the parameter estimation becomes more inaccurate.     

玻色-爱因斯坦凝聚系统的量子Fisher信息与混沌

量子Fisher信息作为经典Fisher信息的自然推广,与量子信息中的纠缠判断具有密切联系.在表现为典型量子混沌特征的受击两分量玻色-爱因斯坦凝聚系统中,研究了与经典相空间对应的纠缠和量子Fisher信息动力学性质. 结果表明,初次撞击后的系统量子态是纠缠的,与初态所处相空间中的混乱程度无关.而量子Fisher信息的动力学演化对系统初态非常敏感,当初态处于混沌区域时,量子Fisher信息值比初态处于规则区域时大.利用这种较好的量子-经典对应关系,得到量子Fisher信息可以刻画量子混沌的结论. 关键词： 量子Fisher信息 玻色-爱因斯坦凝聚 量子混沌 量子-经典对应     

光与物质相互作用系统中的量子Fisher信息和自旋压缩

Fisher信息是估计理论中的重要概念,最近发现与量子信息中的纠缠判据具有密切联系.非旋波近似条件下,Dicke模型经典相空间表现为混沌动力学特征.本文详细考察了Dicke模型描述的光与物质相互作用系统中量子Fisher信息和自旋压缩动力学特性.结果表明:在短时瞬态情况下,无论初态处于规则区域还是混沌区域系统均表现为纠缠性质;但在长时稳态情况下,初态处于规则区域时系统纠缠消失,而初态处于混沌区域时系统则一直存在纠缠.通过与系统自旋压缩动力学性质相比较,发现量子Fisher信息可以更有效地刻画量子混沌.进一步考察初态处于规则和混沌区域时系统密度矩阵和纯度的动力学演化特性,发现混沌导致系统退相干现象发生,说明量子Fisher信息对混沌更敏感.     

Quantum derivation of the excess noise factor in lasers with non-orthogonal eigenmodes

By generalizing recently obtained results we calculate the excess noise factor (Petermann factor) for a laser system with non-orthogonal eigenmodes. The quantum consistency of the calculation is shown through the explicit conservation of input-output commutation rules. As a result of the calculation, the excess noise in the lasing mode is shown to depend on the laser gain below threshold, and on the noise analysis frequency below and above threshold. Received: 27 October 1998 / Received in final form: 11 March 1999     

Stability of soliton lattice phase in the bilayer quantum Hall state under tilted magnetic fields

The bilayer quantum Hall (QH) state at the filling factor ν=1 shows various fascinating quantum phenomena due to the layer degree of freedom called ‘pseudospin’. We report an experimental evidence of the soliton lattice (SL) phase, which is a domain structure of pseudospin, by the appearance of a local maximum of magnetoresistance near the ν=1 QH state. We investigate the stability of the SL phase by changing B and the total electron density n_T. Detailed magnetotransport measurements under tilted magnetic fields were carried out to obtain a B–n_T plane phase diagram containing the C, IC and SL phases. We found the SL phase is only stable at low n_T region. Namely, the C–SL–IC phase transition occurs only at low n_T region as B increases. On the contrary, the C–IC phase transition directly occurs without passing through the SL phase at high n_T region.     

Monte Carlo simulation of overdamped motion in a double well potential under the influence of coloured noise

We present a Monte Carlo simulation algorithm for evaluating the stationary probability and the mean and the variance of first passage times in any dynamical system under the influence of additive coloured Gaussian and Marcovian noise (Ornstein-Uhlenbeck process). Our algorithm generates the Ornstein-Uhlenbeck process by a superposition of a finite number of random telegraph processes. We obtain our results from a direct evaluation of the trajectories. We apply our method to the overdamped motion of a particle in a double well potential. We compare our simulation results with various analytic approximations for the stationary probability and the mean first passage times.