Estimating Non-Gaussianity of a Quantum State by Measuring Orthogonal Quadratures

We derive the lower bounds for a non-Gaussianity measure based on quantum relative entropy (QRE). Our approach draws on the observation that the QRE-based non-Gaussianity measure of a single-mode quantum state is lower bounded by a function of the negentropies for quadrature distributions with maximum and minimum variances. We demonstrate that the lower bound can outperform the previously proposed bound by the negentropy of a quadrature distribution. Furthermore, we extend our method to establish lower bounds for the QRE-based non-Gaussianity measure of a multimode quantum state that can be measured by homodyne detection, with or without leveraging a Gaussian unitary operation. Finally, we explore how our lower bound finds application in non-Gaussian entanglement detection.     

n型金属氧化物半导体场效应晶体管噪声非高斯性研究

基于n型金属氧化物半导体场效应晶体管（nMOSFET）噪声的数涨落模型,采用高阶统计量双相干系数平方和研究了nMOSFET噪声的非高斯性.通过对nMOSFET实际测试噪声的分析,发现nMOSFET器件噪声存在非高斯性;小尺寸器件噪声的非高斯性强于大尺寸器件;在器件的强反型线性区,其非高斯性随着漏压的增加而增加.文中还通过蒙特卡罗模拟和中心极限定理理论对nMOSFET噪声的非高斯性作了深入的探讨. 关键词： 噪声 非高斯性 n型金属氧化物半导体场效应晶体管 氧化层陷阱     

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 non-Gaussianity measures according to the metric axioms and point out that the sine distance is the best candidate among them.     

Lattice calculation of non-gaussian density perturbations from the massless preheating inflationary model

If light scalar fields are present at the end of inflation, their nonequilibrium dynamics such as parametric resonance or a phase transition can produce non-Gaussian density perturbations. We show how these perturbations can be calculated using nonlinear lattice field theory simulations and the separate universe approximation. In the massless preheating model, we find that some parameter values are excluded while others lead to acceptable but observable levels of non-Gaussianity. This shows that preheating can be an important factor in assessing the viability of inflationary models.     

Diagnosis and impacts of non-Gaussianity of innovations in data assimilation

Most of the atmospheric and oceanic data assimilation (DA) schemes rely on the Best Linear Unbiased Estimator (BLUE), which is sub-optimal if errors of assimilated data are non-Gaussian, thus calling for a full Bayesian data assimilation. This paper contributes to the study of the non-Gaussianity of errors in the observational space. Possible sources of non-Gaussianity range from the inherent statistical skewness and positiveness of some physical observables (e.g. moisture, chemical species), the nonlinearity, both of the data assimilation models and of the observation operators among others. Deviations from Gaussianity can be justified from a priori hypotheses or inferred from statistical diagnostics of innovations (observation minus background), leading to consistency relationships between the error statistics. From samples of observations and backgrounds as well as their specified error variances, we evaluate some measures of the innovation non-Gaussianity, such as the skewness, kurtosis and negentropy. Under the assumption of additive errors and by relating statistical moments from both data errors and innovations, we identify potential sources of the innovation non-Gaussianity. These sources range from: (1) univariate error non-Gaussianity, (2), nonlinear correlations between errors, (3) spatio-temporal variability of error variances (heteroscedasticity) and (4) multiplicative noise. Observational and background errors are often assumed independent. This leads to variance-dependent bounds for the skewness and the kurtosis of errors. From innovation statistics, we assess the potential DA impact of some scenarios of non-Gaussian errors. This impact is measured through the mean square difference between the BLUE and the Minimum Variance Unbiased Estimator (MVUE), obtained with univariate observations and background estimates. In order to accomplish this, we compute maximum entropy probability density functions (pdfs) of the errors, constrained by the first four order moments. These pdfs are then used to compute the Bayesian posterior pdf and the MVUE. The referred impact is studied for a large range of statistical moments, being higher for skewed innovations and growing in average with the skewness of data errors, specially if the skewnesses have the same sign. An application has been performed to the quality-accepted ECMWF innovations of brightness temperatures of a set of High Resolution Infrared Sounder (HIRS) channels. In this context, the MVUE has led in some extreme cases to a potential reduction of 20%-60% of the posterior error variance as compared to the BLUE, specially for extreme values of the innovations.     

利用累积量理论量化双模压缩贝尔态的非高斯特性

根据相空间函数的累积量理论,提出了玻色量子态非高斯性的量化工具.利用该量具研究了四个压缩贝尔纠缠态的非高斯特性.结果表明:高斯操作能显著的改变这些态的非高斯特性.此外,也研究了这些量子态二阶关联函数的四阶累积量.     

Toward the detection of gravitational waves under non-Gaussian noises I. Locally optimal statistic

After reviewing the standard hypothesis test and the matched filter technique to identify gravitational waves under Gaussian noises, we introduce two methods to deal with non-Gaussian stationary noises. We formulate the likelihood ratio function under weakly non-Gaussian noises through the Edgeworth expansion and strongly non-Gaussian noises in terms of a new method we call Gaussian mapping where the observed marginal distribution and the two-body correlation function are fully taken into account. We then apply these two approaches to Student’s t-distribution which has a larger tails than Gaussian. It is shown that while both methods work well in the case the non-Gaussianity is small, only the latter method works well for highly non-Gaussian case.     

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.     

Nondiffusive transport in plasma turbulence: a fractional diffusion approach

Numerical evidence of nondiffusive transport in three-dimensional, resistive pressure-gradient-driven plasma turbulence is presented. It is shown that the probability density function (pdf) of tracer particles' radial displacements is strongly non-Gaussian and exhibits algebraic decaying tails. To model these results we propose a macroscopic transport model for the pdf based on the use of fractional derivatives in space and time that incorporate in a unified way space-time nonlocality (non-Fickian transport), non-Gaussianity, and nondiffusive scaling. The fractional diffusion model reproduces the shape and space-time scaling of the non-Gaussian pdf of turbulent transport calculations. The model also reproduces the observed superdiffusive scaling.     

Stochastic resonance of a periodically driven neuron under non-Gaussian noise

We investigate the first-passage-time statistics of the integrate-fire neuron model driven by a sub-threshold harmonic signal superposed with a non-Gaussian noise. Here, we considered the noise as the result of a random multiplicative process displaced from the origin by an additive term. Such a mechanism generates a power-law distributed noise whose characteristic decay exponent can be finely tuned. We performed numerical simulations to analyze the influence of the noise non-Gaussian character on the stochastic resonance condition. We found that when the noise deviates from Gaussian statistics, the resonance condition occurs at weaker noise intensities, achieving a minimum at a finite value of the distribution function decay exponent. We discuss the possible relevance of this feature to the efficiency of the firing dynamics of biological neurons, as the present result indicates that neurons would require a lower noise level to detect a sub-threshold signal when its statistics departs from Gaussian.     

Inflation with multiple sound speeds: A model of multiple DBI type actions and non-Gaussianities

In this Letter we study adiabatic and isocurvature perturbations in the frame of inflation with multiple sound speeds involved. We suggest this scenario can be realized by a number of generalized scalar fields with arbitrary kinetic forms. These scalars have their own sound speeds respectively, so the propagations of field fluctuations are individual. Specifically, we study a model constructed by two DBI type actions. We find that the critical length scale for the freezing of perturbations corresponds to the maximum sound horizon. Moreover, if the mass term of one field is much lighter than that of the other, the entropy perturbation could be quite large and so may give rise to a growth outside sound horizon. At cubic order, we find that the non-Gaussianity of local type is possibly large when entropy perturbations are able to convert into curvature perturbations. We also calculate the non-Gaussianity of equilateral type approximately.     

Superdiffusion and non-Gaussian statistics in a driven-dissipative 2D dusty plasma

Anomalous diffusion and non-Gaussian statistics are detected experimentally in a two-dimensional driven-dissipative system. A single-layer dusty plasma suspension with a Yukawa interaction and frictional dissipation is heated with laser radiation pressure to yield a structure with liquid ordering. Analyzing the time series for mean-square displacement, superdiffusion is detected at a low but statistically significant level over a wide range of temperatures. The probability distribution function fits a Tsallis distribution, yielding q, a measure of nonextensivity for non-Gaussian statistics.     

Non-Gaussianities in New Ekpyrotic Cosmology

The new ekpyrotic model is an alternative scenario of the early Universe which relies on a phase of slow contraction before the big bang. We calculate the 3-point and 4-point correlation functions of primordial density perturbations and find a generically large non-Gaussian signal, just below the current sensitivity level of cosmic microwave background experiments. This is in contrast with slow-roll inflation, which predicts negligible non-Gaussianity. The model is also distinguishable from alternative inflationary scenarios that can yield large non-Gaussianity, such as Dirac-Born-Infeld inflation and the simplest curvatonlike models, through the shape dependence of the correlation functions. Non-Gaussianity therefore provides a distinguishing and testable prediction of New Ekpyrotic Cosmology.     

A test model for fluctuation-dissipation theorems with time-periodic statistics

The recently developed time-periodic fluctuation-dissipation theorem (FDT) provides a very convenient way of addressing the climate change of atmospheric systems with seasonal cycle by utilizing statistics of the present climate. A triad nonlinear stochastic model with exactly solvable first and second order statistics is introduced here as an unambiguous test model for FDT in a time-periodic setting. This model mimics the nonlinear interaction of two Rossby waves forced by baroclinic processes with a zonal jet forced by a polar temperature gradient. Periodic forcing naturally introduces the seasonal cycle into the model. The exactly solvable first and second order statistics are utilized to compute both the ideal mean and variance response to the perturbations in forcing or dissipation and the quasi-Gaussian approximation of FDT (qG-FDT) that uses the mean and the covariance in the equilibrium state. The time-averaged mean and variance qG-FDT response to perturbations of forcing or dissipation is compared with the corresponding ideal response utilizing the triad test model in a number of regimes with various dynamical and statistical properties such as weak or strong non-Gaussianity and resonant or non-resonant forcing. It is shown that even in a strongly non-Gaussian regime, qG-FDT has surprisingly high skill for the mean response to the changes in forcing. On the other hand, the performance of qG-FDT for the variance response to the perturbations of dissipation is good in the near-Gaussian regime and deteriorates in the strongly non-Gaussian regime. The results here on the test model should provide useful guidelines for applying the time-periodic FDT to more complex realistic systems such as atmospheric general circulation models.     

D-Concurrence Bounds for Pair Coherent States

Pair coherent state can be regarded as a state of a two-mode radiation field such that the wave function is non-Gaussian and infinite dimensional, too. Since the entanglement for high dimensional mixed states is difficult to calculate, it is necessary to find bound for entanglement measures. In this paper, some features of quantum entanglement for the pair coherent state are studied and also the upper and lower bounds for D-concurrence (a new entanglement measure) over this state are obtained.     

贝叶斯频率估计中频率的先验分布对有色噪声作用的影响

在贝叶斯参数估计理论框架下,研究了被测参数的先验分布对有色噪声的抑制作用.选择一个受1/f~α型谱密度有色噪声影响的自旋1/2量子比特作为量子探测系统来估计一个磁场强度的大小,利用贝叶斯代价函数的动力学演化来评判估计的精度,重点研究先验概率分布对噪声非高斯性的限制作用.研究发现:当先验概率的不确定度比较大时,有色噪声的非高斯性对频率估计精度的影响比较小;当先验概率的不确定度比较小时,有色噪声的非高斯性对频率估计精度的影响比较大.     

Non-classical Properties of Photon-Added Compass State

We investigate the observable non-classical features of the photon-added compass state (PACS) by its sub-Poissonian statistics, such as the Mandel’s parameter, second-order correlation function, photon-number distribution and the quasi-probability distribution functions, peculiarly the negativity in the Wigner distribution of the PACS as the specific non-classical features. We study the squeezing properties of the PACS and find the PACS does not show squeezing properties of the quadrature. Finally, we give the non-Gaussianity of the PACS by the fidelity between the PACS and the squeezed coherent state (SCS).     

On the incorporation of cubic and hexagonal interfacial energy anisotropy in phase field models using higher order tensor terms

In this paper, we show how to incorporate cubic and hexagonal anisotropies in interfacial energies in phase field models; this incorporation is achieved by including up to sixth rank tensor terms in the free energy expansion, assuming that the free energy is only a function of coarse-grained composition, its gradient, curvature and aberration. We derive the number of non-zero and independent components of these tensors. Further, by demanding that the resultant interfacial energy is positive definite for inclusion of each of the tensor terms individually, we identify the constraints imposed on the independent components of these tensors. The existing results in the invariant group theory literature can be used to simplify the process of construction of some (but not all) of the higher order tensors. Finally, we derive the relevant phase field evolution equations and describe some preliminary results from our 1D simulations.     

Estimate for the doppler shift of a non-Gaussian signal upon coherent detection of scattered optical radiation in a turbulent atmosphere

A non-Gaussian model for estimating the radial velocity of turbulent flows in the atmosphere for coherent detection of scattered optical radiation is proposed. The model was obtained based on a theoretical approach that includes results of the statistical analysis of a pulse Doppler lidar signal in a turbulent medium, as well as on the perturbation-theory methods that have been developed in the theory of probability and mathematical statistics. It is shown that the estimate of the Doppler shift in the first-order perturbation theory is a sum of a regular component and two conditional fluctuation components—Gaussian and non-Gaussian ones. In the case of a homogeneous and isotropic turbulence, the estimate of the radial wind velocity is approximately equal to its true average value. The statistical uncertainty in measurements of the average radial wind velocity is determined by the behavior of conditional Gaussian and non-Gaussian components and significantly depends on the state of atmospheric turbulence. It is shown that basic equations of the non-Gaussian model in the limit case coincide with formulas of the local and nonlocal models, as well as with those of the Gaussian model.