Classical Correlations vs Quantum Correlations—Similarities, Differences, Opportunities

Classical Correlations were founded in 1900 by Karl Pearson and have since been applied as a statistical tool in virtually all sciences. Quantum correlations go back to Albert Einstein et al. in 1935 and Erwin Schrödinger’s responses shortly after. In this paper, we contrast classical with quantum correlations. We find that classical correlations are weaker than quantum correlations in the CHSH framework. With respect to correlation matrices, the trace of classical correlation matrices is dissimilar to quantum density matrices. However, the off-diagonal terms have equivalent interpretations. We contrast classical dynamic (i.e., time evolving) stochastic correlation with dynamic quantum density matrices and find that the off-diagonal elements, while different in nature, have similar interpretations. So far, due to the laws of quantum physics, no classical correlations are applied to the quantum spectrum. However, conversely, quantum correlations are applied in classical environments such as quantum computing, cryptography, metrology, teleportation, medical imaging, laser technology, the quantum Internet and more.

Quantum correlations and entanglement in coupled optomechanical resonators with photon hopping via Gaussian interferometric power analysis

Quantum correlations that surpass entanglement are of great importance in the realms of quantum information processing and quantum computation.Essentially,for quantum systems prepared in pure states,it is difficult to differentiate between quantum entanglement and quantum correlation.Nonetheless,this indistinguishability is no longer holds for mixed states.To contribute to a better understanding of this differentiation,we have explored a simple model for both generating and measuring these quantum correlations.Our study concerns two macroscopic mechanical resonators placed in separate Fabry–Pérot cavities,coupled through the photon hopping process.this system offers a comprehensively way to investigate and quantify quantum correlations beyond entanglement between these mechanical modes.The key ingredient in analyzing quantum correlation in this system is the global covariance matrix.It forms the basis for computing two essential metrics:the logarithmic negativity(E_(N)^(m))and the Gaussian interferometric power(P_(G)^(m)).These metrics provide the tools to measure the degree of quantum entanglement and quantum correlations,respectively.Our study reveals that the Gaussian interferometric power(P_(G)^(m))proves to be a more suitable metric for characterizing quantum correlations among the mechanical modes in an optomechanical quantum system,particularly in scenarios featuring resilient photon hopping.

Dynamics of Non-Markovianity, Quantum Correlations and Information Scrambling of Three Qubits Systems Interacting via Rashba Interaction

The behavior of the quantum correlations, information scrambling and the non-Markovianity of three entangling qubits systems via Rashba is discussed. The results showed that, the three physical quantities oscillate between their upper and lower bounds, where the number of oscillations increases as the Rashba interaction strength increases. The exchanging rate of these three quantities depends on the Rashba strength, and whether the entangled state is generated via direct/indirect interaction. Moreover, the coherence parameter can be used as a control parameter to maximize or minimize the three physical quantities.

Evaluation of frictional pressure drop correlations for air-water and air-oil two-phase flow in pipeline-riser system

Accurate prediction of the frictional pressure drop is important for the design and operation of subsea oil and gas transporting system considering the length of the pipeline. The applicability of the correlations to pipeline-riser flow needs evaluation since the flow condition in pipeline-riser is quite different from the original data where they were derived from. In the present study, a comprehensive evaluation of 24prevailing correlation in predicting frictional pressure drop is carried out based on experimentally measured data of air-water and air-oil two-phase flows in pipeline-riser. Experiments are performed in a system having different configuration of pipeline-riser with the inclination of the downcomer varied from-2°to-5°to investigated the effect of the elbow on the frictional pressure drop in the riser. The inlet gas velocity ranges from 0.03 to 6.2 m/s, and liquid velocity varies from 0.02 to 1.3 m/s. A total of885 experimental data points including 782 on air-water flows and 103 on air-oil flows are obtained and used to access the prediction ability of the correlations. Comparison of the predicted results with the measured data indicate that a majority of the investigated correlations under-predict the pressure drop on severe slugging. The result of this study highlights the requirement of new method considering the effect of pipe layout on the frictional pressure drop.

Study of baryon number transport dynamics and strangeness conservation effects using Ω-hadron correlations

In nuclear collisions at RHIC energies, an excess of Ω hyperons over ■ is observed, indicating that Ω has a net baryon number despite s and s quarks being produced in pairs. The baryon number in Ω may have been transported from the incident nuclei and/or produced in the baryon-pair production of Ω with other types of anti-hyperons such as Ξ. To investigate these two scenarios, we propose to measure the correlations between Ω and K and between Ω and anti-hyperons. We use two versions, the default and string-melting, of a multiphase transport(AMPT) model to illustrate the method for measuring the correlation and to demonstrate the general shape of the correlation. We present the Ω-hadron correlations from simulated Au+Au collisions at ■ =7.7 and 14.6 Ge V and discuss the dependence on the collision energy and on the hadronization scheme in these two AMPT versions. These correlations can be used to explore the mechanism of baryon number transport and the effects of baryon number and strangeness conservation on nuclear collisions.

Spatial correlations in time and frequency domains between chlorophyll-a concentration and environmental factors in the Bohai Sea

Based on the reconstructed MODIS data and ECMWF reanalysis data from 2003 to 2021,spatial correlations between chlorophyll a(Chl a)and sea surface temperature(SST),photosynthetically available radiation(PAR),aerosol optical thickness(AOT),and wind speed(WS)in the Bohai Sea were analyzed from the perspective of time domain and frequency domain.Results indicate that the frequency domain analysis was more conducive to revealing the correlations between Chl a and environmental factors.The spatial pattern of time-domain correlations was similar to the isobaths of the Bohai Sea,which was positive in shallow waters and negative in deep waters for SST,PAR,and AOT,and was reversed for WS.Frequency-domain correlations were obtained by performing Fourier Transform and were higher than correlations in time domain.The spatial distributions indicated that the effects of SST and PAR on Chl a were greater than AOT and WS in the Bohai Sea.Additionally,cross-spectrum analysis was applied to explore the response relationships.A depth-dependent pattern was shown in correlations and time lags,indicating that the influential mechanism of environmental factors on Chl-a concentration is related to seawater depth.

Variational data encoding and correlations in quantum-enhanced machine learning

Leveraging the extraordinary phenomena of quantum superposition and quantum correlation,quantum computing offers unprecedented potential for addressing challenges beyond the reach of classical computers.This paper tackles two pivotal challenges in the realm of quantum computing:firstly,the development of an effective encoding protocol for translating classical data into quantum states,a critical step for any quantum computation.Different encoding strategies can significantly influence quantum computer performance.Secondly,we address the need to counteract the inevitable noise that can hinder quantum acceleration.Our primary contribution is the introduction of a novel variational data encoding method,grounded in quantum regression algorithm models.By adapting the learning concept from machine learning,we render data encoding a learnable process.This allowed us to study the role of quantum correlation in data encoding.Through numerical simulations of various regression tasks,we demonstrate the efficacy of our variational data encoding,particularly post-learning from instructional data.Moreover,we delve into the role of quantum correlation in enhancing task performance,especially in noisy environments.Our findings underscore the critical role of quantum correlation in not only bolstering performance but also in mitigating noise interference,thus advancing the frontier of quantum computing.

Spatial correlations in ground motion intensity measuring from the 2023 Türkiye earthquake

When evaluating an area's seismic risk or resilience,it is necessary to use the spatial correlation to analyze the ground motion parameters of multiple sites together in an earthquake.These two large earthquakes in Türkiye provided the possibility for spatial correlation analysis of ground motion intensity measurements in this area.Based on the strong motion records provided by The Disaster and Emergency Management Authority of Türkiye(AFAD),this study uses the local ground motion prediction equation in Türkiye to give spatial correlation analysis of Intensity Measurements.This study gives an exponential model based on a semivariogram and compares it with the correlation model obtained from previous studies.

Pressure drop of structured packing in pilot column and comparison to common correlations

Packed columns are widely used in the chemical industry such as absorption,stripping,distillation,and extraction in the production of e.g.organic chemicals,and pharmaceuticals.Pressure loss and pressure drop correlations are of special interest when it comes to the hydrodynamic properties of a column.The pressure loss across the column is of interest in the design phase when the size of the blower to drive the gas stream through the column has to be decided.The loading point and flooding point are also influenced by the pressure loss and the area of operation is determined from these points.This work examines four different correlations on pressure drop.The correlations are(i)Ergun’s equation(1952),(ii)an improved version of Ergun’s equation by Stichlmair,Bravo,and Fair(1989),(iii)an equation developed by Billet and Schultes(1999),and(iv)an equation by Rocha,Bravo,and Fair(1993).The complexity of the correlations is increasing in the mentioned order,Ergun’s equation being the simplest one.This study investigates if the more complicated correlations give better predictions to pressure drop in packed columns.This is determined by comparing the correlations to experimental data for pressure drop in a packed column with 8.2 m of structured packing using water as the liquid and atmospheric air as the gas.Seven experiments were carried out for determining the pressure drop in the column with liquid flows varying from 0 to 500 kg·h^(-1).At constant liquid flow,the gas flow was varied from approximately 10 to 70 kg·h^(-1).The pressure drop across the non-wetted column was best described by the correlation by Rocha et al.while the pressure drop for liquid flows from 100 to 500 kg·h^(-1)was,in general,best described by Stichlmair’s equation.For an irrigated column,the highest deviation was a predicted pressure drop 69.6%lower than measured.The best prediction was 0.1%higher than the measured.This study shows,surprisingly,that for a system of water and atmospheric air,complicated correlations on pressure drop determination do not provide better estimates than simple equations.

Dominant factors in MiniCone, CPT and pile correlations: A data‐based approach

The cone penetration test(CPT)contributes to the design and analysis of piles regarding geometry,installation effect,and pile capacity(shaft and toe resistance).MiniCone,as an alternative to CPT sounding,has been used to carry outfield and laboratory investigations by physical modeling.More tests can be practically carried out through light equipment and small soil mass,involving fewer errors caused by boundary conditions.Furthermore,it can be used for in situ testing,such as quality control,assessment of ground improvement,and subgrade characterization.A database comprising MiniCone and CPT records infield and physical modeling is proposed with a variety of cone diameters.The case study records in the database have been obtained from 140 tests compiled from data from 26 sources.The sources include the results of 20 physical modelings andfield data from six sites in 10 countries.The data comprise MiniCone and CPT cone tip resistance(qc),and sleeve friction(fs).The different cones are used in sandy,silty sand,and clayey soils via simple chambers(1 g),calibration chambers,and frustum confining vessels.In addition,correlations were found in penetration records in terms of physical modeling types,cone diameters,penetration rates,and soil densities.Moreover,qc and fs are related to capacities of pile toes and shafts using proper correlation coefficients less than unity,respectively.Correlations and dominant factors in geotechnical practice between MiniCone,CPT,and pile have been reviewed and discussed.

Vacuum Correlations, Detector Efficiency Fluctuations and Classical Dynamic Violations of CH-Inequality

We study in this paper the possible influence of vacuum fluctuations on photo detection and its background noise in Bell tests. We analyze its consequences on the standard statistical analysis of data showing that it is not fulfilled anymore the conventional hypothesis of a Poisson like probability density distribution of single photodetection events. We assume that vacuum fluctuations are due to real and measurable fluctuating fields, as recently confirmed experimentally, and that their non null correlations outside the light cone contribute to photon coincidence rates making them time dependent. We introduce a generalized Bell like correlation function which contains a new term due to supposed vacuum induced photon counting events. We deduce then a generalization of CH-inequality which takes in account the effect of these vacuum electric fields on detector efficiency. We predict an apparatus temperature fluctuations during photon detection which we suggest could be observed by looking for colored noise thermal emission of the photodetectors, generalizing the standard white noise prediction of C.S.L. models on wave function collapse postulate. We discuss an experimental test of this prediction, based on the idea of inducing a thermal wave on the whole quantum detectors, aimed to observe time dependent deviations from standard stationary statistical predictions of Quantum Mechanics.

Correlations among core species corresponding to the clinical staging of periodontitis

The correlation between microbiota plays a vital role in the progression of periodontal disease.This study investigated the in situ interaction networks between periodontal pathogens in periodontal and peri-implant disease.We used quantitative real-time polymerase chain reaction and Pearson’s correlation coefficients to quantify the copy numbers and correlations of four oral core species—Fusobacterium nucleatum,Porphyromonas gingivalis,Prevotella intermedia,and Streptococcus gordonii—from 80 subgingival sites(healthy and with periodontitis or gingivitis)in patients with periodontitis,and 68 subgingival sites(healthy and with periodontitis,gingivitis,peri-implantitis,or peri-implant mucositis)in patients with implants.The highest bacterial counts were observed for Porphyromonas gingivalis and Prevotella intermedia at all the sites.Within the same cohorts,the bacterial loads were greater at diseased sites than at healthy sites.Bacterial counts did not differ among clinical sites in the same group(P>0.05)but differed between periodontitis and peri-implant mucositis sites in the two groups.Porphyromonas gingivalis,F.nucleatum,and Prevotella intermedia had strong correlations at gingivitis and healthy sites and moderate correlations at periodontitis sites in patients with periodontitis.In patients with implants,Prevotella intermedia,F.nucleatum,and S.gordonii had strong correlations only at peri-implantitis sites.Also,based on metagenomic analysis,F.nucleatum and Prevotella intermedia were significantly correlated at the subgingival plaque in peri-implantitis and periodontitis samples.Our results suggest that variations in microbe-microbe interactions in subgingival plaque reflect changes in the progression of periodontal disease,providing a new perspective for understanding the mechanisms of periodontitis and peri-implantitis.

Site selective 5f electronic correlations inβ-uranium

We investigate the electronic structure ofβ-uranium,which has five nonequivalent atomic sites in its unit cell,by means of the density functional theory plus Hubbard-U correction with U from linear response calculation.It is found that the 5f electronic correlations inβ-uranium are moderate.More interestingly,their strengths are site selective,depending on the local atomic environment of the present uranium atom.As a consequence,the occupation matrices and partial 5f density of states ofβ-uranium manifest site dependence.In addition,the complicate experimental structure ofβ-uranium could be well reproduced within this theoretical framework.

Emergence of correlations in twisted monolayer-trilayer graphene heterostructures

Twisted bilayer graphene heterostructures have recently emerged as a well-established platform for studying strongly correlated phases,such as correlated insulating,superconducting,and topological states.Extending this notion to twisted multilayer graphene heterostructures has exhibited more diverse correlated phases,as some fundamental properties related to symmetry and band structures are correspondingly modified.Here,we report the observations of correlated states in twisted monolayer-trilayer(Bernal stacked)graphene heterostructures.Correlated phases at integer fillings of the moire unit cell are revealed at a high displacement field and stabilized with a moderate magnetic field on the electron-doping side at a twist angle of 1.45°,where the lift of degeneracy at the integer fillings is observed in the Landau fan diagram.Our results demonstrate the effectiveness of moire engineering in an extended structure and provide insights into electric-field tunable correlated phases.

Space-time correlations of passive scalar in Kraichnan model

We consider the two-point,two-time(space-time)correlation of passive scalar R(r,τ)in the Kraichnan model under the assumption of homogeneity and isotropy.Using the fine-gird PDF method,we find that R(r,τ)satisfies a diffusion equation with constant diffusion coefficient determined by velocity variance and molecular diffusion.Itssolution can be expressed in terms of the two-point,one time correlation of passive scalar,i.e.,R(r,0).Moreover,the decorrelation o R(k,τ),which is the Fourier transform of R(r,τ),is determined byR(k,0)and a diffusion kernal.

Maintenance Optimization for EMU Trains Considering Environmental Impacts and Correlations

The complexity of the actual operating environment of EMU trains and the interaction between the reliability of system components have become a huge challenge for the maintenance scheduling of EMU trains. In response to these problems, the evolution of reliability and failure rate under the influence of environmental factors, failure correlations and economy correlations is analyzed. We assume bogie systems form the EMU train in series. The failure correlation matrix of the bogie systems is modeled. With the lowest total maintenance cost as the optimization objective, a decision-making model for EMU train maintenance is established. A dynamic maintenance strategy is proposed for the model, which can improve maintenance plans efficiently. Artificial bee colony algorithm is applied to further iteratively optimize the threshold parameters in the strategy. The results are calculated and verified by a numerical example. The results show the effectiveness of the maintenance decision model. The dynamic maintenance strategy in this paper is compared with the traditional opportunistic maintenance strategy. The proposed maintenance strategy outperforms the traditional opportunistic maintenance strategy in the numerical example.

Correlations in Werner States

Werner states are paradigmatic examples of quantum states and play an innovative role in quantum information theory. In investigating the correlating capability of Werner states, we find the curious phenomenon that quantum correlations, as quantified by the entanglement of formation, may exceed the total correlations, as measured by the quantum mutual information. Consequently, though the entanglement of formation is so widely used in quantifying entanglement, it cannot be interpreted as a consistent measure of quantum correlations per se if we accept the folklore that total correlations are measured （or rather upper bounded） by the quantum mutual information.

Estimates of Heritability and Genetic Correlations for Growth Traits in Chinese Shrimp Fenneropenaeus chinensis

[Objective] The aim was to estimate the heritability and genetic correlations of growth traits of Chinese shrimp Fenneropenaeus chinensis so as to provide basis and technical parameters for the breeding and selecting of Chinese shrimp.[Method] 51 full-sib families（including 35 half-sib families）of the Chinese shrimp F.chinensis were obtained by artificial insemination.Four growth traits of these families were measured,including body length,cephalothorax length,abdorminal segment length and body weight.According to quantitative genetics theory,the heritability of each growth trait,genetic and phenotypic correlation among these traits was statistically studied.[Result] The heritability was 0.36-0.51 for body length,0.14-0.24 for cephalothorax length,0.25-0.50 for abdominal segment length,and 0.04-0.29 for body weight.High and positive genetic correlations were obtained among growth traits.The genetic correlation between body weight and abdominal segment length was the highest（0.92）,followed by body length and abdominal segment length（0.91）,body length and body weight（0.88）,body weight and cephalothorax length（0.87）,abdominal segment length and cephalothorax length（0.86）,while the genetic correlation between body length and cephalothorax length was the lowest（0.83）.[Conclusion] The phenotypic correlation of body length,cephalothorax length,abdorminal segment length and body weight of Chinese shrimp F.chinensis were from 0.80 to 0.90 with extremely significant difference（P0.01）among the four growth traits by t-test.

Repeat Sequences and Base Correlations in Human Y Chromosome Palindromes

On the basis of information theory and statistical methods, we use mutual information, n- tuple entropy and conditional entropy, combined with biological characteristics, to analyze the long range correlation and short range correlation in human Y chromosome palindromes. The magnitude distribution of the long range correlation which can be reflected by the mutual information is PS〉PSa〉PSb （P5a and P5b are the sequences that replace solely Alu repeats and all interspersed repeats with random uneorrelated sequences in human Y chromosome palindrome 5, respectively）; and the magnitude distribution of the short range correlation which can be reflected by the n-tuple entropy and the conditional entropy is PS〉P5a〉PSb〉random uncorrelated sequence. In other words, when the Alu repeats and all interspersed repeats replace with random uneorrelated sequence, the long range and short range correlation decrease gradually. However, the random nncorrelated sequence has no correlation. This research indicates that more repeat sequences result in stronger correlation between bases in human Y chromosome. The analyses may be helpful to understand the special structures of human Y chromosome palindromes profoundly.

Age–age correlations and early selection for growth traits in 40 half-sib families of Larix principis-rupprechtii

Larix principis-rupprechtii Mayr is a dominant species in coniferous forests of North China.However,early selection of L.principis-rupprechtii for growth traits is poorly characterised.To explore the optimal selection age for this species,heights(HT)and diameters at breast(DBH)of 40 half-sib families were measured at ages 3,12,22,and 28 years in a progeny test population established in the town of Kangjiahui,Shanxi Province.Age trends in heritability,age–age genetic correlations,and early selection efficiency for height and DBH were analysed.The individual heritability of these growth traits varied over time,and maximized at different ages(0.55 at age 12 for HT and 0.48 at age 28 for DBH).The age–age genetic correlations were always positive,and the majority were high(0.790–0.953)between the juvenile and mature ages for HT and DBH.For the same pairs of measurements,HT demonstrated higher age–age genetic correlations than DBH,and both age–age genetic correlation data sets were described well by the linear relationship with the logarithm of the age ratio(r2[0.90).The regression slope for DBH was lower than that for HT.Based on the early selection efficiency estimates,the optimal selection age could be as early as age 6 for DBH and 8–9 years for HT.The results of this study provide information that can be used to assist early selection practices in L.principis-rupprechtii improvement programs in Shanxi Province.