Quantum Fisher information for moving three-level atom

Quantum information technology largely relies on a precious and fragile resource, call quantum entanglement, which exhibits a highly nontrivial manifestation of the coherent superposition of states of composite quantum systems. In this article, we discuss the correlation between the quantum entanglement measured by the von Neumann entropy and atomic quantum Fisher information by taking account the case of moving three-level atom. Our results show that there is a monotonic relation between the atomic quantum Fisher information and entanglement in the case of non-moving atom. On the other hand, we find that the atomic quantum Fisher information and entanglement exhibit an opposite changement behavior during the time evolution in the presence of atomic motion.     

Modeling time criticality of information

In this paper, we continue the research on formal treatment of attributes of information, based on the computational approach. In this scenario, the usefulness of advisory information is measured by the decrease in complexity of a problem we need to solve. We propose to model the time criticality via usefulness of a piece of information which is received during the computation. As a modeling tool, we use deterministic finite automata.     

Quantum Fisher information,quantum entanglement and correlation close to quantum critical phenomena

In this paper, we investigate the quantum Fisher information (QFI), quantum entanglement, quantum correlation and quantum phase transition (QPT) within the one-dimensional transverse Ising model by exploiting quantum renormalization-group method. The results show that quantum Fisher information, quantum entanglement, quantum correlation can evolve to two saturated values which exhibit QPT at the critical point after several iterations of the renormalization. Meanwhile, we find quantum entanglement or correlation can be detected perfectly by means of quantum Fisher information. Besides, it cannot capture any information about the system in the paramagnetic phase in view of quantum entanglement and correlation. Contrarily, it is evident the QFI is always nonzero even if the system is in the paramagnetic phase, i.e., the QFI can also be utilized as a highly favorable measure of quantum information in a broad of quantum spin systems. Furthermore, we disclose the nonanalytic and scaling behaviors of quantum Fisher information, which can be taken as a representation of quantum critical characterism.     

Fisher information based progressive censoring plans

In life tests, the progressive Type-II censoring methodology allows for the possibility of censoring a number of units each time a failure is observed. This results in a large number of possible censoring plans, depending on the number of both censoring times and censoring numbers. Employing maximum Fisher Information as an optimality criterion, optimal plans for a variety of lifetime distributions are determined numerically. In particular, exact optimal plans are established for some important lifetime distributions. While for some distributions, Fisher information is invariant with respect to the censoring plan, results for other distributions lead us to hypothesize that the optimal scheme is in fact always a one-step method, restricting censoring to exactly one point in time. Depending on the distribution and its parameters, this optimal point of censoring can be located at the end (right censoring) or after a certain proportion of observations. A variety of distributions is categorized accordingly. If the optimal plan is a one-step censoring scheme, the optimal proportion is determined. Moreover, the Fisher information as well as the expected time till the completion of the experiment for the optimal one-step censoring plan are compared with the respective quantities of both right censoring and simple random sampling.     

Fisher information based progressive censoring plans

In life tests, the progressive Type-II censoring methodology allows for the possibility of censoring a number of units each time a failure is observed. This results in a large number of possible censoring plans, depending on the number of both censoring times and censoring numbers. Employing maximum Fisher Information as an optimality criterion, optimal plans for a variety of lifetime distributions are determined numerically. In particular, exact optimal plans are established for some important lifetime distributions. While for some distributions, Fisher information is invariant with respect to the censoring plan, results for other distributions lead us to hypothesize that the optimal scheme is in fact always a one-step method, restricting censoring to exactly one point in time. Depending on the distribution and its parameters, this optimal point of censoring can be located at the end (right censoring) or after a certain proportion of observations. A variety of distributions is categorized accordingly. If the optimal plan is a one-step censoring scheme, the optimal proportion is determined. Moreover, the Fisher information as well as the expected time till the completion of the experiment for the optimal one-step censoring plan are compared with the respective quantities of both right censoring and simple random sampling.     

Quantum information transmission

We present a scheme of quantum information transmission, which transmits the quantum information contained in a single qubit via the quantum correlation shared by two parties (a two-qubit channel), whose quantum discord is non-zero. We demonstrate that quantum correlation, which may have no entanglement, is sufficient to transmit the information needed to reconstruct a quantum state. When the correlation matrix of the two-qubit channel is of full rank (rank three), the information of the qubit (in either a mixed state or a pure state) can be transmitted. The quantum discord of a channel with rank larger than or equal to three is always non-zero. Therefore, non-zero quantum discord is also necessary for our quantum information transmission protocol. The scheme may be useful in remote state tomography and remote state preparation.     

Efficient Monte Carlo computation of Fisher information matrix using prior information

The Fisher information matrix (FIM) is a critical quantity in several aspects of mathematical modeling, including input selection and confidence region calculation. Analytical determination of the FIM in a general setting, especially in nonlinear models, may be difficult or almost impossible due to intractable modeling requirements or/and intractable high-dimensional integration.To circumvent these difficulties, a Monte Carlo simulation based technique, known as resampling algorithm, is usually recommended, in which values of the log-likelihood function or its exact stochastic gradient computed based on a set of pseudo-data vectors are used. The current work proposes an extension of this resampling algorithm in order to enhance the statistical qualities of the estimator of the FIM. This modified resampling algorithm is useful in those cases when some elements of the FIM are analytically known from prior information and the rest of the elements are unknown. The estimator of the FIM resulting from the proposed algorithm simultaneously preserves the analytically known elements and reduces variances of the estimators of the unknown elements. This is achieved by capitalizing on the information contained in the known elements.     

Fisher and Shannon information in finite neural populations

The precision of the neural code is commonly investigated using two families of statistical measures: Shannon mutual information and derived quantities when investigating very small populations of neurons and Fisher information when studying large populations. These statistical tools are no longer the preserve of theorists and are being applied by experimental research groups in the analysis of empirical data. Although the relationship between information-theoretic and Fisher-based measures in the limit of infinite populations is relatively well understood, how these measures compare in finite-size populations has not yet been systematically explored. We aim to close this gap. We are particularly interested in understanding which stimuli are best encoded by a given neuron within a population and how this depends on the chosen measure. We use a novel Monte Carlo approach to compute a stimulus-specific decomposition of the mutual information (the SSI) for populations of up to 256 neurons and show that Fisher information can be used to accurately estimate both mutual information and SSI for populations of the order of 100 neurons, even in the presence of biologically realistic variability, noise correlations, and experimentally relevant integration times. According to both measures, the stimuli that are best encoded are those falling at the flanks of the neuron's tuning curve. In populations of fewer than around 50 neurons, however, Fisher information can be misleading.     

Quantum symmetrically-private information retrieval

Private information retrieval systems (PIRs) allow a user to extract an item from a database that is replicated over k?1 servers, while satisfying various privacy constraints. We exhibit quantum k-server symmetrically-private information retrieval systems (QSPIRs) that use sublinear communication, do not use shared randomness among the servers, and preserve privacy against honest users and dishonest servers. Classically, SPIRs without shared randomness do not exist at all.     

Optimal short-term population coding: when Fisher information fails

Efficient coding has been proposed as a first principle explaining neuronal response properties in the central nervous system. The shape of optimal codes, however, strongly depends on the natural limitations of the particular physical system. Here we investigate how optimal neuronal encoding strategies are influenced by the finite number of neurons N (place constraint), the limited decoding time window length T (time constraint), the maximum neuronal firing rate f(max) (power constraint), and the maximal average rate (f)(max) (energy constraint). While Fisher information provides a general lower bound for the mean squared error of unbiased signal reconstruction, its use to characterize the coding precision is limited. Analyzing simple examples, we illustrate some typical pitfalls and thereby show that Fisher information provides a valid measure for the precision of a code only if the dynamic range (f(min)T, f(max)T) is sufficiently large. In particular, we demonstrate that the optimal width of gaussian tuning curves depends on the available decoding time T. Within the broader class of unimodal tuning functions, it turns out that the shape of a Fisher-optimal coding scheme is not unique. We solve this ambiguity by taking the minimum mean square error into account, which leads to flat tuning curves. The tuning width, however, remains to be determined by energy constraints rather than by the principle of efficient coding.     

Quantum control and information processing

We review the recent developments in quantum control and its contribution to quantum information processing.     

随机颜色直方图的Fisher信息融合及应用

采用在颜色空间的随机划分基础上提取随机直方图从而实现一种以动态方式提取图像颜色分布信息的方法。基于多项费歇尔几何,采用平均延拓的费歇尔信息距离量化随机颜色直方图集合之间综合的信息差异。除了为基于k-近邻的图像分类提供最直接判别元素外,融合的平均信息差异也使得在一个乘积多项流形闭包上学习随机颜色直方图集的集合成为可能。基于颜色特征的图像分类,聚类及可视化等任务此时可在减少集上完成。在ALOI数据集的部分图像集上获得的实验结果证实了方法的有效性。     

基于信息增益的最优组合因子Fisher判别法

线性判别分类器是一种有效的模式分析技术,其中以Fisher判别法准则应用最广,目前已有多种改进线性提取方法。引进信息增益,建立基于信息增益的最优组合因子判别分类器,实现最优组合因子判别分类器的优化。实验结果表明优化后的分类器有效剔除了冗余因子,具有良好的分类准确率。     

Fisher Linear Discriminant Analysis for text-image combination in multimedia information retrieval

With multimedia information retrieval, combining different modalities – text, image, audio or video provides additional information and generally improves the overall system performance. For this purpose, the linear combination method is presented as simple, flexible and effective. However, it requires to choose the weight assigned to each modality. This issue is still an open problem and is addressed in this paper.     

Protection of quantum Fisher information in entangled states via classical driving

Quantum entanglement can offer a quadratic enhancement in the precision of parameter estimation. We here study the protection of quantum Fisher information (QFI) of the phase parameter in entangled-atom states within the framework of independently dissipative environments and driven individually by classical fields. It is shown that the QFI of the phase parameter can be protected effectively only when the classical fields that drive all atoms are suitably strong, and if one of them vanishes or is very weak, then the ability of protection loses, no matter how strong the other driving fields are. We also study the evolution of fidelity of the entangled state itself and find that though the protections of QFI and quantum states are two different notions, the method can also be used to protect quantum states effectively when the driving fields are suitably strong.     

On minimum Fisher information distributions with restricted support and fixed variance

Fisher information is of key importance in estimation theory. It also serves in inference problems as well as in the interpretation of many physical processes. The mean-squared estimation error for the location parameter of a distribution is bounded by the inverse of the Fisher information associated with this distribution. In this paper we look for minimum Fisher information distributions with a restricted support. More precisely, we study the problem of minimizing the Fisher information in the set of distributions with fixed variance defined on a bounded subset S of R or on the positive real line. We show that the solutions of the underlying differential equation can be expressed in terms of Whittaker functions. Then, in the two considered cases, we derive the explicit expressions of the solutions and investigate their behavior. We also characterize the behavior of the minimum Fisher information as a function of the imposed variance.     

Noisy metrology: a saturable lower bound on quantum Fisher information

Quantum Information Processing - We present a general problem of quantum entanglement quantified by von Neumann entropy for N-level atomic system. Time evolution of state vector of the entire...     

颜色共生矩阵的Fisher信息度量及识别应用

基于多项流形的黎曼几何,提出一个在矩阵流形框架下度量颜色共生矩阵信息差异并将其应用于目标识别的新方法。对于给定的颜色量化水平和每个像素局部邻域,该方法将一幅彩色图像的任意两个颜色通道中共生的颜色建模为一个潜在的多项分布的概率实现。通过基于紧化的共生频率嵌入,可将每幅图像等同为一个积矩阵流形上的一点,其中每个因子流形被赋予了从对应的多项流形上诱导的Fisher信息距离度量。对于一个识别任务,测试样本与训练样本间的匹配通过先在每个因子流形上使用最近邻分类器进行标签预测然后在积流形上进行多数投票完成。在GT彩色人脸库和COIL-100目标库上获得的出色的识别效果验证了该方法的有效性。     

Enhancing quantum coherence and quantum Fisher information by quantum partially collapsing measurements

We consider the enhancement effect of quantum partially collapsing measurements, i.e., weak measurement and quantum measurement reversal, on quantum coherence and quantum Fisher information, both of which are transmitted through a spin-chain channel. For the state parameter lying in the region \((\pi /2,\ \pi )\), weak measurement can enhance quantum coherence and quantum Fisher information. For the state parameter lying in the region \((0,\ \pi /2)\), quantum coherence and quantum Fisher information can be enhanced by quantum measurement reversal combined with weak measurement. We assume the probabilistic nature of the method should be responsible for the enhancement.