Witnessing quantum phase transition in a non-Hermitian trapped ion system via quantum Fisher information

Quantum Fisher information is used to witness the quantum phase transition in a non-Hermitian trapped ion system with balanced gain and loss,from the viewpoint of quantum parameter estimation.We formulate a general non-unitary dynamic of any two-level non-Hermitian system in the form of state vector.The sudden change in the dynamics of quantum Fisher information occurs at an exceptional point characterizing quantum criticality.The dynamical behaviors of quantum Fisher information are classified into two different ways which depends on whether the system is located in symmetry unbroken or broken phase regimes.In the phase regime where parity and time reversal symmetry are unbroken,the oscillatory evolution of quantum Fisher information is presented,achieving better quantum measurement precision.In the broken phase regime,quantum Fisher information undergoes the monotonically decreasing behavior.The maximum value of quantum estimation precision is obtained at the exceptional point.It is found that the two distinct kinds of behaviors can be verified by quantum entropy and coherence.Utilizing quantum Fisher information to witness phase transition in the non-Hermitian system is emphasized.The results may have potential applications to non-Hermitian quantum information technology.

Sensor management based on fisher information gain

Multi-sensor system is becoming increasingly important in a variety of military and civilian applications. In general, single sensor system can only provide partial information about environment while multi-sensor system provides a synergistic effect, which improves the quality and availability of information. Data fusion techniques can effectively combine this environmental information from similar and/or dissimilar sensors. Sensor management, aiming at improving data fusion performance by controlling sensor behavior, plays an important role in a data fusion process. This paper presents a method using fisher information gain based sensor effectiveness metric for sensor assignment in multi-sensor and multi-target tracking applications. The fisher information gain is computed for every sensor-target pairing on each scan. The advantage for this metric over other ones is that the fisher information gain for the target obtained by multi-sensors is equal to the sum of ones obtained by the individual sensor, so standard transportation problem formulation can be used to solve this problem without importing the concept of pseudo sensor. The simulation results show the effectiveness of the method.

Quantum Fisher information and spin squeezing in one-axis twisting model

We investigate the dependence of the average parameter estimation precision （APEP）, which is defined by the quantum Fisher information, on the polar angle of the initial coherent spin state ｜θ0,φ0〉 in a one-axis twisting model. Jin et al. [New J. Phys. 11 （2009） 073049] found that the spin squeezing sensitively depends on the polar angle θ0 of the initial coherent spin state. We show explicitly that the APEP is robust to the initial polar angle θ0 in the vicinity of π/2 and a near- Heisenberg limit 2IN in quantum single-parameter estimation may still be achieved for states created with the nonlinear evolution of the nonideal coherent spin states θ0- π/2. Based on this model, we also consider the effects of the collective dephasing on spin squeezing and the APEE

Generalized Uncertainty Inequalities on Fisher Information Associated with LCT

Uncertainty principle plays an important role in multiple fields such as physics,mathem-atics,signal processing,etc.The linear canonical transform(LCT)has been used widely in optics and information processing and so on.In this paper,a few novel uncertainty inequalities on Fisher information associated with linear canonical transform are deduced.These newly deduced uncer-tainty relations not only introduce new physical interpretation in signal processing,but also build the relations between the uncertainty lower bounds and the LCT transform parameters a,b,c and d for the first time,which give us the new ideas for the analysis and potential applications.In addi-tion,these new uncertainty inequalities have sharper and tighter bounds which are the generalized versions of the traditional counterparts.Furthermore,some numeric examples are given to demon-strate the efficiency of these newly deduced uncertainty inequalities.

Logarithm Versus Square Root： Comparing Quantum Fisher Information

In classical statistics, the Fisher information is unique in the sense that it is essentially the only monotone Riemannian metric on the space of probability densities. In quantum theory, this uniqueness breaks down, and there are many natural quantum analogues of the Fisher information, among which two particular versions distinguish themselves by their intuitive and informational significance： The first has its origin in the skew information introduced by Wigner and Yanase in 1963 in the context of quantum measurement, and is defined via the square root of the density operator. The second arises from Helstrom＇s study of quantum detection in 1967, and is defined via the symmetric logarithmic derivative. The aim of this paper Js to compare these two versions of quantum Fisher information, and to establish two informational inequalities relating them.

An Informational Approach to The Sinusoidal Law of Photon Polarization

The photon polarization law p(theta) = sin(2)theta is derived from a simple informational consideration by two methods: The first is via an intuitive principle of minimum Fisher information, the second is via a symmetry and invariance argument. The results demonstrate that in photon polarization, Nature has a tendency to hide herself as deep as possible while obeying some regular 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.

OPERATOR-VALUED FREE FISHER INFORMATION OF RANDOM MATRICES

The free Fisher information of an operator random matrix is studied. When the covariance of a random matrix is a conditional expectation, the free Fisher information of such a matrix is the double of this conditional expectation’s Watatani index.

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.

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.

FREE FISHER INFORMATION AND AMALGAMATED FREENESS

The notion of operator-valued free Fisher information was introduced.It is a generalization of free Fisher information which was defined by D.Voiculescu on tracial von Neumann algebras.It is proved that the operator-valued free Fisher information is closely related to amalgamated freeness,i.e.,the operator-valued free Fisher information of some random variables is additive if and only if these random variables are a free family with amalgamation over a subalgebra.Cramer-Rao inequality in operator-valued settings is also obtained.

Fisher information for generalized Rayleigh distribution in ranked set sampling design with application to parameter estimation

In the current paper,we considered the Fisher information matrix from the generalized Rayleigh distribution(GR)distribution in ranked set sampling(RSS).The numerical results show that the ranked set sample carries more information about λ and α than a simple random sample of equivalent size.In order to give more insight into the performance of RSS with respect to(w.r.t.)simple random sampling(SRS),a modified unbiased estimator and a modified best linear unbiased estimator(BLUE)of scale and shape λ and α from GR distribution in SRS and RSS are studied.The numerical results show that the modified unbiased estimator and the modified BLUE of λ and α in RSS are significantly more efficient than the ones in SRS.

Quantum Fisher Information of Two-Level Atomic System under the Influence of Thermal Field, Intrinsic Decoherence, Stark Effect and Kerr-Like Medium

In this paper, we have proposed the numerical calculations to study the quantum entanglement (QE) of moving two-level atom interacting with a coherent and the thermal field influenced by intrinsic decoherence (ID), Kerr medium (non-linear) and the Stark effect. The wave function of the complete system interacting with a coherent and the thermal field is calculated numerically affected by ID, Kerr (non-linear) and Stark effects. It has been seen that the Stark, Kerr, ID and the thermal environment have a significant effect during the time evolution of the quantum system. Quantum Fisher information (QFI) and QE decrease as the value of the ID parameter is increased in the thermal field without the atomic movement. It is seen that QFI and von Neumann entropy (VNE) show an opposite and periodic response in the presence of atomic motion. The non-linear Kerr medium has a more prominent and significant effect on the QE as the value of the Kerr parameter is decreased. At smaller values of the non-linear Kerr parameter, the VNE increases, however, QFI decreases, so QFI and VNE have a monotonic connection with one another. As the value of the Kerr parameter is increased, the effect of non-linear Kerr doesn’t stay critical on both QFI and QE. However, a periodic response of QE is seen because of the atomic movement which becomes modest under natural impacts. Moreover, it has been seen that QFI and QE rot soon at the smaller values of the Stark parameter. However, as the value of the Stark parameter is increased, the QFI and QE show periodic response even when the atomic movement is absent.

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.

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.

Optimal observation configuration of UAVs based on angle and range measurements and cooperative target tracking in three-dimensional space

This article investigates the optimal observation configuration of unmanned aerial vehicles(UAVs) based on angle and range measurements, and generalizes predecessors' researches in two dimensions into three dimensions. The relative geometry of the UAVs-target will significantly affect the state estimation performance of the target, the cost function based on the Fisher information matrix(FIM) is used to derive the FIM determinant of UAVs' observation in three-dimensional space, and the optimal observation geometric configuration that maximizes the determinant of the FIM is obtained. It is shown that the optimal observation configuration of the UAVs-target is usually not unique, and the optimal observation configuration is proved for two UAVs and three UAVs in three-dimension. The long-range over-the-horizon target tracking is simulated and analyzed based on the analysis of optimal observation configuration for two UAVs. The simulation results show that the theoretical analysis and control algorithm can effectively improve the positioning accuracy of the target. It can provide a helpful reference for the design of over-the-horizon target localization based on UAVs.

Asymptotic properties and expectation-maximization algorithm for maximum likelihood estimates of the parameters from Weibull-Logarithmic model

In this article, we consider a lifetime distribution, the Weibull-Logarithmic distri- bution introduced by [6]. We investigate some new statistical characterizations and properties. We develop the maximum likelihood inference using EM algorithm. Asymptotic properties of the MLEs are obtained and extensive simulations are conducted to assess the performance of parameter estimation. A numerical example is used to illustrate the application.

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.

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.