Non-Gaussianity detection of single-mode rotationally symmetric quantum states via cumulant method

The non-Gaussianity of quantum states incarnates an important resource for improving the performance of continuous-variable quantum information protocols.We propose a novel criterion of non-Gaussianity for single-mode rotationally symmetric quantum states via the squared Frobenius norm of higher-order cumulant matrix for the quadrature distribution function.As an application,we study the non-Gaussianities of three classes of single-mode symmetric non-Gaussian states:a mixture of vacuum and Fock states,single-photon added thermal states,and even/odd Schr¨odinger cat states.It is shown that such a criterion is faithful and effective for revealing non-Gaussianity.We further extend this criterion to two cases of symmetric multi-mode non-Gaussian states and non-symmetric single-mode non-Gaussian states.

Developing improved measures of non-Gaussianity and Gaussianity for quantum states based on normalized Hilbert–Schmidt distance

Non-Gaussianity of quantum states is a very important source for quantum information technology and can be quantified by using the known squared Hilbert–Schmidt distance recently introduced by Genoni et al.(Phys. Rev. A 78 042327(2007)). It is, however, shown that such a measure has many imperfects such as the lack of the swapping symmetry and the ineffectiveness evaluation of even Schr?dinger-cat-like states with small amplitudes. To deal with these difficulties, we propose an improved measure of non-Gaussianity for quantum states and discuss its properties in detail. We then exploit this improved measure to evaluate the non-Gaussianities of some relevant single-mode non-Gaussian states and multi-mode non-Gaussian entangled states. These results show that our measure is reliable. We also introduce a modified measure for Gaussianity following Mandilara and Cerf(Phys. Rev. A 86 030102(R)(2012)) and establish a conservation relation of non-Gaussianity and Gaussianity of a quantum state.

A Non-Stationary Beam-Enabled Stochastic Channel Model and Characterization over Non-Reciprocal Beam Patterns

The multiple-input multiple-output(MIMO)-enabled beamforming technology offers great data rate and channel quality for next-generation communication.In this paper,we propose a beam channel model and enable it with time-varying simulation capability by adopting the stochastic geometry theory.First,clusters are generated located within transceivers'beam ranges based on the Mate?rn hardcore Poisson cluster process.The line-of-sight,singlebounce,and double-bounce components are calculated when generating the complex channel impulse response.Furthermore,we elaborate on the expressions of channel links based on the propagation-graph theory.A birth-death process consisting of the effects of beams and cluster velocities is also formulated.Numerical simulation results prove that the proposed model can capture the channel non-stationarity.Besides,the non-reciprocal beam patterns yield severe channel dispersion compared to the reciprocal patterns.

The Limit Distribution of Stochastic Evolution Equations Driven by-Stable Non-Gaussian Noise

We study the distribution limit of a class of stochastic evolution equation driven by an additive-stable Non-Gaussian process in the case of α∈(1,2).We prove that,under suitable conditions,the law of the solution converges weakly to the law of a stochastic evolution equation with an additive Gaussian process.

Efficient simulation of spatially correlated non-stationary ground motions by wavelet-packet algorithm and spectral representation method

Although the classical spectral representation method(SRM)has been widely used in the generation of spatially varying ground motions,there are still challenges in efficient simulation of the non-stationary stochastic vector process in practice.The first problem is the inherent limitation and inflexibility of the deterministic time/frequency modulation function.Another difficulty is the estimation of evolutionary power spectral density(EPSD)with quite a few samples.To tackle these problems,the wavelet packet transform(WPT)algorithm is utilized to build a time-varying spectrum of seed recording which describes the energy distribution in the time-frequency domain.The time-varying spectrum is proven to preserve the time and frequency marginal property as theoretical EPSD will do for the stationary process.For the simulation of spatially varying ground motions,the auto-EPSD for all locations is directly estimated using the time-varying spectrum of seed recording rather than matching predefined EPSD models.Then the constructed spectral matrix is incorporated in SRM to simulate spatially varying non-stationary ground motions using efficient Cholesky decomposition techniques.In addition to a good match with the target coherency model,two numerical examples indicate that the generated time histories retain the physical properties of the prescribed seed recording,including waveform,temporal/spectral non-stationarity,normalized energy buildup,and significant duration.

Seismic safety assessment with non-Gaussian random processes for train-bridge coupled systems

Extensive high-speed railway(HSR)network resembled the intricate vascular system of the human body,crisscrossing mainlands.Seismic events,known for their unpredictability,pose a significant threat to both trains and bridges,given the HSR’s extended operational duration.Therefore,ensuring the running safety of train-bridge coupled(TBC)system,primarily composed of simply supported beam bridges,is paramount.Traditional methods like the Monte Carlo method fall short in analyzing this intricate system efficiently.Instead,efficient algorithm like the new point estimate method combined with moment expansion approximation(NPEM-MEA)is applied to study random responses of numerical simulation TBC systems.Validation of the NPEM-MEA’s feasibility is conducted using the Monte Carlo method.Comparative analysis confirms the accuracy and efficiency of the method,with a recommended truncation order of four to six for the NPEM-MEA.Additionally,the influences of seismic magnitude and epicentral distance are discussed based on the random dynamic responses in the TBC system.This methodology not only facilitates seismic safety assessments for TBC systems but also contributes to standard-setting for these systems under earthquake conditions.

An improved predictive deconvolution based on maximization of non-Gaussianity

The predictive deconvolution algorithm （PD）, which is based on second-order statistics, assumes that the primaries and the multiples are implicitly orthogonal. However, the seismic data usually do not satisfy this assumption in practice. Since the seismic data （primaries and multiples） have a non-Gaussian distribution, in this paper we present an improved predictive deconvolution algorithm （IPD） by maximizing the non-Gaussianity of the recovered primaries. Applications of the IPD method on synthetic and real seismic datasets show that the proposed method obtains promising results.

Non-Gaussianity dynamics of two-mode squeezed number states subject to different types of noise based on cumulant theory

We provide a measure to characterize the non-Gaussianity of phase-space function of bosonic quantum states based on the cumulant theory. We study the non-Gaussianity dynamics of two-mode squeezed number states by analyzing the phase-averaged kurtosis for two different models of decoherence： amplitude damping model and phase damping model.For the amplitude damping model, the non-Gaussianity is very fragile and completely vanishes at a finite time. For the phase damping model, such states exhibit rich non-Gaussian characters. In particular, we obtain a transition time that such states can transform from sub-Gaussianity into super-Gaussianity during the evolution. Finally, we compare our measure with the existing measures of non-Gaussianity under the independent dephasing environment.

Non-Gaussianity and decoherence of generalized photon-added coherent state as a Hermite-excited coherent state

Generalized photon-added coherent state （GPACS） is creation and annihilation operations on the coherent state. obtained by repeatedly acting the combination of Bose It is found that GPACS can be regarded as a Hermiteexcited coherent state due to its normalization factor related to a Hermite polynomial. In addition, we adopt the Hilbert-Schmidt distance to quantify the non-Gaussian character of GPACS and discuss the decoherence of GPACS in dissipative channel by studying the loss of nonclassicality in reference of the negativity of Wigner function.

Alternative non-Gaussianity measures for quantum states based on quantum fidelity

We propose three alternative measures for non-Gaussianity of quantum states: sine distance, Bures angle, and Bures distance, which are based on quantum fidelity introduced by Wang [Phys. Lett. A 373 58(2008)]. Using them, we evaluate the non-Gaussianity of some relevant single-mode and two-mode non-Gaussian states and find a good consistency of the three examined measures. In addition, we show that such metrics can exactly quantify the degree of Gaussianity of even Schrödinger-cat-like states of small amplitudes that can not be measured by other known non-Gaussianity measures such as the Hilbert–Schmidt metric and the relative entropy metric. We make a comparative study between all existing nonGaussianity measures according to the metric axioms and point out that the sine distance is the best candidate among them.

Hurricane damage assessment for residential construction considering the non-stationarity in hurricane intensity and frequency

Natural hazards such as hurricanes may cause extensive economic losses and social disruption for civil structures and infrastructures in coastal areas, implying the importance of understanding the construction performance subjected to hurricanes and assessing the hurricane damages properly. The intensity and frequency of hurricanes have been reported to change with time due to the potential impact of climate change.In this paper, a probability-based model of hurricane damage assessment for coastal constructions is proposed taking into account the non-stationarity in hurricane intensity and frequency. The nonhomogeneous Poisson process is employed to model the non-stationarity in hurricane occurrence while the non-stationarity in hurricane intensity is reflected by the time-variant statistical parameters(e.g., mean value and/or standard deviation), with which the mean value and variation of the cumulative hurricane damage are evaluated explicitly. The Miami-Dade County, Florida, USA, is chosen to illustrate the hurricane damage assessment method proposed in this paper. The role of non-stationarity in hurricane intensity and occurrence rate due to climate change in hurricane damage is investigated using some representative changing patterns of hurricane parameters.

Maximum Correntropy Kalman Filtering for Non-Gaussian Systems With State Saturations and Stochastic Nonlinearities

This paper tackles the maximum correntropy Kalman filtering problem for discrete time-varying non-Gaussian systems subject to state saturations and stochastic nonlinearities. The stochastic nonlinearities, which take the form of statemultiplicative noises, are introduced in systems to describe the phenomenon of nonlinear disturbances. To resist non-Gaussian noises, we consider a new performance index called maximum correntropy criterion(MCC) which describes the similarity between two stochastic variables. To enhance the “robustness” of the kernel parameter selection on the resultant filtering performance, the Cauchy kernel function is adopted to calculate the corresponding correntropy. The goal of this paper is to design a Kalman-type filter for the underlying systems via maximizing the correntropy between the system state and its estimate. By taking advantage of an upper bound on the one-step prediction error covariance, a modified MCC-based performance index is constructed. Subsequently, with the assistance of a fixed-point theorem, the filter gain is obtained by maximizing the proposed cost function. In addition, a sufficient condition is deduced to ensure the uniqueness of the fixed point. Finally, the validity of the filtering method is tested by simulating a numerical example.

Non-Gaussian quantum states generation and robust quantum non-Gaussianity via squeezing field

Recent studies show that quantum non-Gaussian states or using non-Gaussian operations can improve entanglement distillation, quantum swapping, teleportation, and cloning. In this work, employing a strategy of non-Gaussian operations（namely subtracting and adding a single photon）, we propose a scheme to generate non-Gaussian quantum states named single-photon-added and-subtracted coherent（SPASC） superposition states by implementing Bell measurements, and then investigate the corresponding nonclassical features. By squeezed the input field, we demonstrate that robustness of nonGaussianity can be improved. Controllable phase space distribution offers the possibility to approximately generate a displaced coherent superposition states（DCSS）. The fidelity can reach up to F ≥ 0.98 and F ≥ 0.90 for size of amplitude z = 1.53 and 2.36, respectively.

Non-Gaussianity of Racetrack Inflation Models

In this paper,we use the result in[C.Y.Sun and D.H.Zhang,arXiv:astro-ph/0510709]to calculate thenon-Gaussianity of the racetrack models in[J.J.Blanco-Pillado,et al.,JHEP 0411(2004)063;arXiv:hep-th/0406230]and[J.J.Blanco-Pillado,et al.,arXiv:hep-th/0603129].The two models give different non-Gaussianities.Both of themare reasonable.However,we find that,for multi-field inflationary models with the non-trivial metric of the field space,the condition of the slow-roll cannot guarantee small non-Gaussianities.

Estimating the evolution of sea state non-Gaussianity based on a phase-resolving model

The occurrence of rogue waves is closely related to the non-Gaussianity of sea states,and this non-Gaussianity can be estimated using corresponding two-dimensional wave spectra.This paper presents an approach to non-Gaussianity estimation based on a phase-resolving model called the high-order spectral method(HOSM).Based on numerous HOSM simulations,a set of precalculated non-Gaussianity indicators was established that could be applied to real sea states without any calibration of spectral shapes.With a newly developed extraction approach,the indicators for given two-dimensional wave spectra could then be conveniently extracted from the precalculated dataset.The feasibility of the newly developed approach in a real wave environment is verified.Using the estimation approach,phase-resolved non-Gaussianity can now be illustrated throughout the evolution of sea states of interest,not just at a few specific times;and the level of non-Gaussianity at any time in a duration can be identified according to the statistics(e.g.,quantities)of the phase-resolved indicators,that are obtained throughout the duration concerned.

Non-Gaussian approach:Withstanding loss and noise of multi-scattering underwater channel for continuous-variable quantum teleportation

Underwater quantum communication plays a crucial role in ensuring secure data transmission and extensible quantum networks in underwater environments.However,the implementation of such applications encounters challenges due to the light attenuation caused by the complicated natural seawater.This paper focuses on employing a model based on seawater chlorophyll-a concentration to characterize the absorption and scattering of light through quantum channels.We propose a multi-scattering random channel model,which demonstrates characteristics of the excess noise in different propagation directions of communication links.Furthermore,we consider the fidelity of a continuous-variable quantum teleportation through seawater channel.To enhance transmission performance,non-Gaussian operations have been conducted.Numerical simulations show that incorporating non-Gaussian operations enables the protocol to achieve higher fidelity transmission or lower fidelity fading rates over longer transmission distances.

Gaussian Sum PHD Filtering Algorithm for Nonlinear Non-Gaussian Models

A new multi-target filtering algorithm, termed as the Gaussian sum probability hypothesis density （GSPHD） filter, is proposed for nonlinear non-Gaussian tracking models. Provided that the initial prior intensity of the states is Gaussian or can be identified as a Gaussian sum, the analytical results of the algorithm show that the posterior intensity at any subsequent time step remains a Gaussian sum under the assumption that the state noise, the measurement noise, target spawn intensity, new target birth intensity, target survival probability, and detection probability are all Gaussian sums. The analysis also shows that the existing Gaussian mixture probability hypothesis density （GMPHD） filter, which is unsuitable for handling the non-Gaussian noise cases, is no more than a special case of the proposed algorithm, which fills the shortage of incapability of treating non-Gaussian noise. The multi-target tracking simulation results verify the effectiveness of the proposed GSPHD.

Towards Near-Field Communications for 6G:Challenges and Opportunities

Extremely large-scale multiple-input multiple-output(XL-MIMO)and terahertz(THz)communications are pivotal candidate technologies for supporting the development of 6G mobile networks.However,these techniques invalidate the common assumptions of far-field plane waves and introduce many new properties.To accurately understand the performance of these new techniques,spherical wave modeling of near-field communications needs to be applied for future research.Hence,the investigation of near-field communication holds significant importance for the advancement of 6G,which brings many new and open research challenges in contrast to conventional far-field communication.In this paper,we first formulate a general model of the near-field channel and discuss the influence of spatial nonstationary properties on the near-field channel modeling.Subsequently,we discuss the challenges encountered in the near field in terms of beam training,localization,and transmission scheme design,respectively.Finally,we point out some promising research directions for near-field communications.

Generation of Non-Gaussian Random Vibration Excitation Signal for Reliability Enhancement Test

During environment testing, the time histories of some dynamic environments follow non-Gaussian distribution. It is always assumed that the random vibration simulated follows Gaussian distribution, because the traditional digital random vibration control system can only supply the random vibration excitation signal of Gaussian. Yo simulate the real environment of product, a method is developed in this paper that can generate non-Gaussian random signal with specified power spectrum density （PSD）, skewness and kurtosis by shot noise. In this way, non-Gaussian random vibration can be produced on traditional electrodynamic shaker. It solves the problems of spectral valley and energy shortage in low frequency on omni-axis shaker. At last, the wavelet is used to analyze the non-Gaussian signal

Theory of Quantum Dissipation in a Class of Non-Gaussian Environments

In this work we construct a novel dissipaton-equation-of-motion （DEOM） theory in quadratic bath coupling environment, based on an extended algebraic statistical quasi-particle approach. To validate the new ingredient of the underlying dissipaton algebra, we derive an extended Zusman equation via a totally different approach. We prove that the new theory, if it starts with the identical setup, constitutes the dynamical resolutions to the extended Zusman equation. Thus, we verify the generalized （non-Gaussian） Wick＇s theorem with dissipatons-pair added. This new algebraic ingredient enables the dissipaton approach being naturally extended to nonlinear coupling environments. Moreover, it is noticed that, unlike the linear bath coupling case, the influence of a non-Gaussian environment cannot be completely characterized with the linear response theory. The new theory has to take this fact into account. The developed DEOM theory manifests the dynamical interplay between dissipatons and nonlinear bath coupling descriptors that will be specified. Numerical demonstrations will be given with the optical line shapes in quadratic coupling environment.