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.

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.

Charm hadron azimuthal angular correlations in Au+Au collisions at ■=200 GeV from parton scatterings

The dynamic evolution of the charm hadron in hot quark matter was studied in the framework of a multiphase transport(AMPT)model.We first reproduced the open charm hadron D0pT spectrum in Au+Au collisions at √sNN=200 GeV by triggering the c c production in AMPT,and then the elliptic flow of charm hadrons was described with different parton cascade cross sections.Charm hadron azimuthal angular correlations were proposed,and they are affected by the different parton crosssection parameter applied in the model,which can facilitate our understanding of the loss of collision energy of charm quarks in hot quark medium and can stimulate further experimental studies.

Vector Correlations and Product Rotational Alignments of Reactions Ca+RBr→CaBr+R(R=CH_(3),C_(2) H_(5) and n-C_(3) H_(7))

The quasiclassical trajectory method is used to study the vector correlations of the reactions Ca＋RBr （R=CH3, C2H5 and n-C3H7Br） and the rotational alignment of product CaBr. The product rotational alignment parameters at different collision energies and the vector correlations between the reagent and product are numerically calculated. The vector correlations are described by using the angle distribution functions P（θr）, P（φr）, P（θr, φr） and the polarization-dependent differential cross sections （PDDCSs）. The peak values of P（θr） of the product CaBr from Ca＋CH3Br are larger than those from Ca＋C2H5Br and Ca＋n-C3H7Br. The peak of P（θr） at φr= 3π/2 is apparently stronger than that at φr= x/2 for the three reactions Ca＋RBr. The calculation results show that the rotational angular momentum of the product CaBr is not only aligned, but also oriented along the direction which is perpendicular to the scattering plane.The product CaBr molecules are strongly scattered forward. The orientation and alignment of the product angular momentum will affect the scattering direction of the product molecules to varying degrees.

Phenotypic correlations of somatic and gonad traits of sea urchins Glyptocidaris crenularis in two sampled periods:first insight into its breeding and aquaculture

Prior knowledge of the correlations among commercially important traits in Glyptocidaris crenularis can be used to guide development of breeding and aquaculture programs for this species.We evaluated the phenotypic correlations between somatic and gonadal traits in G.crenularis during two sample periods(October 2010 and April 2011).The coeffi cients of variation(CV%)for body weight(BW),redness(a*),yellowness(b*),gonad wet weight(GW),and gonad index(GI)were>20% in both periods,while those of other traits were very low.GW was signifi cantly correlated with somatic traits(diameter,height,and body weight)in both periods,although the correlation coeffi cients ranged from 0.473 to 0.636(P<0.01).Gonad moisture content(GC),a*,and lightness(L*)were not signifi cantly correlated with somatic traits(P>0.05).The color trait b* was negatively correlated with somatic traits(test diameter,test height,and body weight)during the period when the gonads were well developed(April 2011,P<0.05).We observed little difference in the nature of the phenotypic correlations between the two sample periods.The high variation in the somatic and gonad weight traits in G.crenularis suggests there is considerable potential for selective breeding.However,our results suggest that gonad quality traits cannot be selected indirectly by selecting for body weight.Our study provides an insight into the method for improving the breeding and aquaculture of G.crenulari.

Detrended Fluctuation Analysis on Correlations of Complex Networks Under Attack and Repair Strategy

We analyze the correlation properties of the Erd6s-Rdnyi random graph （RG） and the Barabdsi-Albert scale-free network （SF） under the attack and repair strategy with detrended fluctuation analysis （DFA）. The maximum degree kmax, representing the local property of the system, shows similar scaling behaviors for random graphs and scale-free networks. The fluctuations are quite random at short time scales but display strong anticorrelation at longer time scales under the same system size N and different repair probability pre. The average degree 〈k〉, revealing the statistical property of the system, exhibits completely different scaling behaviors for random graphs and scale-free networks. Random graphs display long-range power-law correlations. Scale-free networks are uncorrelated at short time scales; while anticorrelated at longer time scales and the anticorrelation becoming stronger with the increase of pre.

Prediction of wall deposition behaviour in a pilot-scale spray dryer using deposition correlations for pipe flows

The particle deposition behaviour of skim milk, water and maltodextrin in the conical section of a pilot-scale spray dryer was predicted using simple correlations for particle depositions in pipes. The predicted particle deposition fluxes of these materials were then compared with the measured deposition fluxes. The predicted particle deposition regimes of the spray dryer were expected to be in the diffusional and mixed (diffusional and inertial) regimes, but the experimental results suggested that the particle deposition was mainly in the inertial regime. Therefore, using the pipe correlations for predicting deposition in a pilot-scale spray dryer suggests that they do not sufficiently represent the actual deposition behaviour. This outcome indicates that a further study of particle flow patterns needs to be carried out using numerical simulations (computational fluid dynamics, CFD) in view of the additional geometrical complexity of the spray dryer.

Breaking the linear correlations for enhanced electrochemical nitrogen reduction by carbon-encapsulated mixed-valence Fe_(7)(PO_(4))_(6)

Electrochemical nitrogen reduction(NRR)is deemed as a consummate answer for the traditional Haber–Bosch technology.Breaking the linear correlations between adsorption and transition-state energies of intermediates is vital to improve the kinetics of ammonia synthesis and obtain a less energy-intensive process.Herein,carbon-encapsulated mixed-valence Fe_(7)(PO_(4))_(6) was prepared and applied as an electrocatalyst for high-efficiency NRR.A dramatic faradaic efficiency(FE)of 36.93%and an NH_(3) production rate of 13.1μg h^(-1) mg_(cat)^(-1) were obtained at-0.3 V versus RHE,superior to nearly all Fe-based catalysts.Experiments and DFT calculations revealed that the superior performance was ascribed to the synergistic effect of mixed-valence iron pair,which braked the linear correlations to improve the kinetics of ammonia from collaborative hydrogenation and*NH_(3) separation.This work proves the feasibility of mixedvalence catalysts for nitrogen reduction and thus opening a new avenue towards artificial nitrogenfixation catalysts.

Horizontal-Longitudinal Correlations of Acoustic Field in Deep Water

The horizontal-longitudinal correlations of the acoustic field in deep water are investigated based on the experi- mental data obtained in the South China Sea. It is shown that the horizontal-longitudinal correlation coefficients in the convergence zone are high, and the correlation length is consistent with the convergence zone width, which depends on the receiver depth and range. The horizontal-longitudinal correlation coefficients in the convergence zone also have a division structure for the deeper receiver. The signals from the second part of the convergence zone are still correlated with the reference signal in the first part. The horizontal-longitudinal correlation coeffi- cients in the shadow zone are lower than that in the convergence zone, and the correlation length in the shadow zone is also much shorter than that in the convergence zone. The numerical simulation results by using the normal modes theory are qualitatively consistent with the experimental results.

Deformation correlations,stress field switches and evolution of an orogenic intersection:The Pan-African Kaoko-Damara orogenic junction,Namibia

Age calibrated deformation histories established by detailed mapping and dating of key magmatic time markers are correlated across all tectono-metamorphic provinces in the Damara Orogenic System.Correlations across structural belts result in an internally consistent deformation framework with evidence of stress field rotations with similar timing,and switches between different deformation events.Horizontal principle compressive stress rotated clockwise ~180°in total during Kaoko Belt evolution,and^135° during Damara Belt evolution.At most stages,stress field variation is progressive and can be attributed to events within the Damara Orogenic System,caused by changes in relative trajectories of the interacting Rio De La Plata,Congo,and Kalahari Cratons.Kaokoan orogenesis occurred earliest and evolved from collision and obduction at ~590 Ma,involving E-W directed shortening,progressing through different transpressional states with ~45° rotation of the stress field to strike-slip shear under NW-SE shortening at ~550-530 Ma.Damaran orogenesis evolved from collision at ~555-550 Ma with NW-SE directed shortening in common with the Kaoko Belt,and subsequently evolved through ~90°rotation of the stress field to NE-SW shortening at ~512-508 Ma.Both Kaoko and Damara orogenic fronts were operating at the same time,with all three cratons being coaxially convergent during the 550-530 Ma period;Rio De La Plata directed SE against the Congo Craton margin,and both together over-riding the Kalahari Craton margin also towards the SE.Progressive stress field rotation was punctuated by rapid and significant switches at ~530-525 Ma,~508 Ma and ~505 Ma.These three events included:(1)Culmination of main phase orogenesis in the Damara Belt,coinciding with maximum burial and peak metamorphism at 530-525 Ma.This occurred at the same time as termination of transpression and initiation of transtensional reactivation of shear zones in the Kaoko Belt.Principle compressive stress switched from NW-SE to NNW-SSE shortening in both Kaoko and Damara Belts at this time.This marks the start of Congo-Kalahari stress field overwhelming the waning Rio De La Plata-Congo stress field,and from this time forward contraction across the Damara Belt generated the stress field governing subsequent low-strain events in the Kaoko Belt.(2)A sudden switch to E-W directed shortening at ~508 Ma is interpreted as a far-field effect imposed on the Damara Orogenic System,most plausibly from arc obduction along the orogenic margin of Gondwana(Ross-Delamerian Orogen).(3)This imposed stress field established a N-S extension direction exploited by decompression melts,switch to vertical shortening,and triggered gravitational collapse and extension of the thermally weakened hot orogen core at ~505 Ma,producing an extensional metamorphic core complex across the Central Zone.