基于量子Fisher信息的量子计量进展

量子计量是超冷原子气体研究中的一个热点领域.超冷原子体系独特的量子性质(量子纠缠)和量子效应有助于大幅度提高待测物理量的测量精度,这已经成为量子精密测量中的共识.量子Fisher信息对该领域的发展起了非常重要的作用.本文首先介绍量子Fisher信息的基本概念和量子计量的主要内容;然后简要回顾这些理论在提高测量精度方面的应用,特别是多粒子量子纠缠态的产生及其判定;再介绍线性和非线性原子干涉仪的相关进展;最后论述量子测量过程中的统计方法的研究进展.     

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.     

Quantum Fisher information width in quantum metrology

In scenarios of quantum metrology, the unitary parametrization process often depends on space directions. How to characterize the sensitivity of parameter estimation to space directions is a natural question. We propose the concept of the quantum Fisher information(QFI) width, which is the difference between the maximum and minimum values of the QFI, to quantitatively study the sensitivity. We find that Fock states, the bosonic coherent states, and the displaced Fock states all have zero widths, indicating that QFI is completely inert over all directions, while the width for the spin state with all spins down or up is equal to the number of particles, so this concept will enable us to choose appropriate directions to make unitary transformation to obtain larger QFI.The QFI width of the displaced quantum states is found to be independent of the magnitude of the displacement for both spin and bosonic systems. We also find some relations between the QFI width and squeezing parameters.     

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.     

Dynamical quantum Fisher information in the Ising model

In terms of quantum Fisher information, we discuss the dynamics of quantity ${\chi }^2$ of the Ising model. The inequality ${\chi }^2<1$ detects the class of entangled states which are useful for sub-shot-noise sensitivity. All the exact dynamics of the expectations of collective spin operators are derived. The minimum ${\chi }^2$ in the plane perpendicular to the mean spin direction is analytically given. We find that ${\chi }^2$ does not depend on the system size $N$ when $N\ge 4$. Except for the periodic points, the evolution states are always entangled and useful for the sub-shot-noise phase estimation.     

Dynamic quantum revivals in phase space

We explain quantum revivals and fractional revivals in phase space of the Fermi?CUlam accelerator. We derive analytic expressions of the Wigner distribution function for the driven system describing quantum interferences in position and momentum space. We assume that the fractional revival times are nonrecurrent under certain conditions and display randomness in the occurrence of the phenomenon at these times.     

基于部分测量增强量子隐形传态过程的量子Fisher信息

量子Fisher信息(QFI)是量子度量学中的一个重要物理量,可给出预估参数精度的最优值.本文研究如何引入弱测量和测量反转操作,来提高有限温环境下以Greenberger-Horne-Zeilinger态作为量子通道的隐形传态过程中的QFI.依据隐形传态过程中量子比特的传输情形,考虑了三种不同方案相应的QFI.首先,通过构造每种量子隐形传态方案的量子线路图,分析了QFI与推广振幅衰减噪声参数的变化关系.随后对各种方案中的受噪声粒子施加弱测量和测量反转操作,并对相应的部分测量参数进行优化,着重探讨了施加最优部分测量操作后QFI的改进量.结果表明,经过优化后的部分测量操作能有效提高有限温环境下量子隐形传态过程输出态的QFI;而且量子系统所处的环境温度越低,QFI的提高效果可越显著.     

Phase damping destroys quantum Fisher information of W states

We study the quantum Fisher information (QFI) of W states in the basic decoherence channels. We show that, as decoherence starts and increases, under i) depolarizing, QFI smoothly decays; ii) amplitude damping, QFI first exhibits a sudden drop to the shot noise level, then decreases to zero and finally increases back to the shot noise level; iii) phase damping, QFI is zero for all non-zero decoherence. We also find that on the contrary to GHZ states, QFI of W states in x and y directions are equal to each other and zero in z direction.     

Preservation of nonclassicality in the continuous-variable quantum teleportation

We first establish the relation between the P-function of the input and output states in the protocol of quantum teleportation of continuous variables of an optical field. We find a condition involving the squeezing parameter and the detector efficiency, under which the P-function of the output state becomes the Q function of the input state such that any nonclassical features in the input state will be eliminated in the teleported state. In particular, we notice that if the homodnye detection efficiency is less than 0.5 the teleported field must be classical even if the entanglement in the quantum channel is perfect.     

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.     

基于量子费希尔信息的纠缠判据

对于几类常见的量子态, 对自旋压缩和量子Fisher信息进行了比较研究.得到量子Fisher信息的表达式,以Fisher信息为基础,给出了量子纠缠的判据,结果表明:比较于自旋压缩,该判据有明显的优势.(1).对于两个Qubit的对称态,该判据与自旋压缩,concurrence完全等价;(2).对于两个Qubit的非对称态的纠缠,自旋压缩不能检验其纠缠,但对于部分态,该判据也能检验;(3).对于Dicke态, 自旋压缩不能检验其纠缠,但该判据能检验且完全等价于concurrence.     

A comparative study of local quantum Fisher information and local quantum uncertainty in Heisenberg XY model

Recently, it has been shown that the quantum Fisher information via local observables and via local measurements (i.e., local quantum Fisher information (LQFI)) is a central concept in quantum estimation and quantum metrology and captures the quantumness of correlations in multi-component quantum system (Kim et al. (2018) [28]). This new discord-like measure is very similar to the quantum correlations measure called local quantum uncertainty (LQU). In the present study, we have revealed that LQU is bounded by LQFI in the phase estimation protocol. Also, a comparative study between these two quantum correlations quantifiers is addressed for the quantum Heisenberg XY model. Two distinct situations are considered. The first one concerns the anisotropic XY model and the second situation concerns isotropic XY model submitted to an external magnetic field. Our results confirm that LQFI reveals more quantum correlations than LQU.     

基于量子费希尔信息的纠缠判据

对于几类常见的量子态, 对自旋压缩和量子Fisher信息进行了比较研究.得到量子Fisher信息的表达式,以Fisher信息为基础,给出了量子纠缠的判据,结果表明:比较于自旋压缩,该判据有明显的优势.(1).对于两个Qubit的对称态,该判据与自旋压缩,concurrence完全等价;(2).对于两个Qubit的非对称态的纠缠,自旋压缩不能检验其纠缠,但对于部分态,该判据也能检验;(3).对于Dicke态, 自旋压缩不能检验其纠缠,但该判据能检验且完全等价于concurrence.     

Local wave-vector, Shannon and Fisher information

It is shown that the local wave-vector gives the connection between the Shannon and Fisher information: the local wave-vector is the gradient of the Shannon information per particle and the square of the local wave-vector is the Fisher information per particle.     

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$\beta$.     

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.     

Quantifying nonclassicality of multimode bosonic fields via skew information

We quantify the nonclassicality of multimode bosonic field states by adopting an information-theoretic approach involving the Wigner-Yanase skew information. The fundamental properties of the quantifier such as convexity, superadditivity, monotonicity, and conservation relations are revealed. The quantifier is illustrated by a variety of typical examples, and applications to the quantification of nonclassical correlations are discussed. Various extensions are indicated.