Different Kinds Of Correlations Research Articles

Quantum Correlation Generation Capability of Experimental Processes

AbstractEinstein–Podolsky–Rosen (EPR) steering and Bell nonlocality illustrate two different kinds of correlations predicted by quantum mechanics. They not only motivate the exploration of the foundation of quantum mechanics, but also serve as important resources for quantum‐information processing in the presence of untrusted measurement apparatuses. Herein, a method for characterizing the creation of EPR steering and Bell nonlocality is introduced for dynamical processes in experiments. It shows that the capability of an experimental process to create quantum correlations can be quantified and identified simply by preparing separable states as test inputs of the process and then performing local measurements on single qubits of the corresponding outputs. This finding enables the construction of objective benchmarks for the two‐qubit controlled operations used to perform universal quantum computation. It demonstrates this utility by examining the experimental capability of creating quantum correlations with the controlled‐phase operations on the IBM Quantum Experience and Amazon Braket Rigetti superconducting quantum computers. The results show that the method provides a useful diagnostic tool for evaluating the primitive operations of nonclassical correlation creation in noisy intermediate scale quantum devices.

Discrimination of textures with spatial correlations and multiple gray levels.

Analysis of visual texture is important for many key steps in early vision. We study visual sensitivity to image statistics in three families of textures that include multiple gray levels and correlations in two spatial dimensions. Sensitivities to positive and negative correlations are approximately independent of correlation sign, and signals from different kinds of correlations combine quadratically. We build a computational model, fully constrained by prior studies of sensitivity to uncorrelated textures and black-and-white textures with spatial correlations. The model accounts for many features of the new data, including sign-independence, quadratic combination, and the dependence on gray-level distribution.

Adaptive Correlation Integration for Deep Image Clustering

Deep clustering methods often estimate data correlations to guide unsupervised learning. However, since different kinds of correlations capture different data characteristics, a strong data correlation may not be appropriate for every case. In this paper, we propose a novel Teacher-Student framework to adaptively estimate correlation and interactively learn a deep clustering model for various data distributions. Specifically, a teacher module mines and integrates various kinds of correlations from different perspectives. To adapt to various cases, we propose a novel Adaptive Integration Gate (ADI-Gate) to selectively and dynamically integrate different data correlations in a teaching-feedback manner. Furthermore, a student module performs unsupervised clustering inference with the estimated correlation and provides a preference for teacher module. We also design a Pairwise-Weighted loss (PW-loss) to enhance high-confident correlation guidance of data pairs during the learning process of student module. In image clustering experiments on four public datasets, our model achieves consistent improvements over state-of-the-art models.

Hierarchy of correlation quantifiers comparable to negativity

Quantum systems generally exhibit different kinds of correlations. In order to compare them on equal footing, one uses the so-called distance-based approach where different types of correlations are captured by the distance to different sets of states. However, these quantifiers are usually hard to compute as their definition involves optimization aiming to find the closest states within the set. On the other hand, negativity is one of the few computable entanglement monotones, but its comparison with other correlations required further justification. Here we place negativity as part of a family of correlation measures that has a distance-based construction. We introduce a suitable distance, discuss the emerging measures and their applications, and compare them to relative entropy-based correlation quantifiers. This work is a step towards correlation measures that are simultaneously comparable and computable.

Entropy production and the role of correlations in quantum Brownian motion

We perform a study on quantum entropy production, different kinds of correlations, and their interplay in the driven Caldeira-Leggett model of quantum Brownian motion. The model, taken with a large but finite number of bath modes, is exactly solvable, and the assumption of a Gaussian initial state leads to an efficient numerical simulation of all desired observables in a wide range of model parameters. Our study is composed of three main parts. We first compare two popular definitions of entropy production, namely the standard weak-coupling formulation originally proposed by Spohn and later on extended to the driven case by Deffner and Lutz, and the always-positive expression introduced by Esposito, Lindenberg and van den Broeck, which relies on the knowledge of the evolution of the bath. As a second study, we explore the decomposition of the Esposito et al. entropy production into system-environment and intra-environment correlations for different ranges of couplings and temperatures. Lastly, we examine the evolution of quantum correlations between the system and the environment, measuring entanglement through logarithmic negativity.

Fundamental Analysis in China: An Empirical Study of the Relationship between Financial Ratios and Stock Prices

The informational context is regularly questioned in a transitional economic regime like the one implemented in China or Vietnam. This article investigates this issue and the predictive power of fundamental analysis in such context and more precisely in a Chinese context with an analysis of 3 different industries (media, power, and steel). Through 3 different kinds of correlation, we examine 25 financial determinants for 60 Chinese listed companies between 2011 and 2015. Our results show that fundamental analysis can effectively be used as an investment tool in transitional economic context. Contrasting with the EMH for which the accounting information is instantaneously integrated into the financial information (stock prices), our study suggests that these two levels of information are not synchronized in China opening therefore a door for a fundamental analysis based prediction. Furthermore, our results also indicate that accounting information illustrates quite well the economic reality since financial reports in each industry can disclose a part of stock value information in line with the economic situation of the industry under consideration.

Transport of correlations in a harmonic chain

We study the propagation of different types of correlations through a quantum bus formed by a chain of coupled harmonic oscillators. This includes steering, entanglement, mutual information, quantum discord, and Bell-like nonlocality. The whole system consists of the quantum bus (propagation medium) and other quantum harmonic oscillators (sources and receivers of quantum correlations) weakly coupled to the chain. We are particularly interested in using the point of view of transport to spot distinctive features displayed by different kinds of correlations. We found, for instance, that there are fundamental differences in the way steering and discord propagate, depending on the way they are defined with respect to the parties involved in the initial correlated state. We analyzed both the closed- and open-system dynamics as well as the role played by thermal excitations in the propagation of the correlations.

Generalized scale-free homophilic network

We propose a simple network growth process where the preferential attachment contains two essential parameters: homophily, namely, the tendency of sites to link with similar ones, and the number of attaching neighbors. It jointly generalizes the Barabási–Albert model and the scale-free homophilic model with a control parameter which tunes the importance of the homophily on preferential attachment process. Our results support a detailed discussion about different kinds of correlation, in special a fitness correlation introduced in this paper, and comparisons between BA model, scale-free homophilic model, and our present model considering its topological properties: degree distribution, time dependence of the connectivity and clustering coefficient.

Unified scheme for correlations using linear relative entropy

A linearized variant of relative entropy is used to quantify in a unified scheme the different kinds of correlations in a bipartite quantum system. As illustration, we consider a two-qubit state with parity and exchange symmetries for which we determine the total, classical and quantum correlations. We also give the explicit expressions of its closest product state, closest classical state and the corresponding closest product state. A closed additive relation, involving the various correlations quantified by linear relative entropy, is derived.

Investigation of quantum and classical correlations in a quantum dot system under decoherence

In this paper, we investigate quantitatively the thermal classical and quantum correlations in an isolated quantum dot system (QDS) including the effects of different parameters. We show that the quantum discord (QD) is more resistant against the temperature effect and might be finite even for higher temperatures in the asymptotic limit. Decoherence in a QDS caused by interaction with its environment is another interesting issue in the quantum information field. Assuming Markovian dynamics for the time evolution, we present noise models for the QDS by using Kraus operators for several noisy channels; in particular bit flip, bit-phase flip, phase flip, and depolarizing channels. By analytical and numerical analyses, we investigate the dynamics of different kinds of correlations, namely, the mutual information, the classical correlation, the entanglement of formation (EOF), and the QD in different channels. The sudden change in behavior in the decay rates of correlations and their immunity against certain decoherences are shown. We explore a symmetry among these channels and provide the decoherence areas for which both classical and quantum correlations remain affected in the QDS.

Detecting quantum and classical correlations using quantum dot system

We investigate the thermal classical and quantum correlations in an isolated quantum dot system (QDS) including the effects of different parameters. The thermal density operator is generated by simplifying the Hamiltonian of the quantum dot to the nature Hamiltonian by integrating and finding the unitary matrix. We find that the quantum discord (QD) is more resistant against temperature effect and might be finite even for higher temperatures in the asymptotic limit. Furthermore, we show that there is an optimal value of temperature such that the different kinds of correlations are maximal. Our results show that QDS is a useful resource and may open new perspectives in different quantum information tasks.

Dynamics of geometric and entropic quantifiers of correlations in open quantum systems

We extend the Hilbert-Schmidt (square norm) distance, previously used to define the geometric quantum discord, to define also geometric quantifiers of total and classical correlations. We then compare the dynamics of geometric and entropic quantifiers of the different kinds of correlations in a non-Markovian open two-qubit system under local dephasing. We find that qualitative differences occur only for quantum discords. This is taken to imply that geometric and entropic discords are not, in general, equivalent in describing the dynamics of quantum correlations. We then show that geometric and entropic quantifiers of total correlations also present qualitative disagreements in the state space. This aspect indicates that the differences found for quantum discord are not attributable to a different separation, introduced by each measure, between the quantum and classical parts of correlations. Finally, we find that the Hilbert-Schmidt distance formally coincides with a symmetrized form of linear relative entropy.

Asymptotic dynamics of quantum discord in open quantum systems

It is well known that quantum entanglement makes certain tasks in quantum information theory possible. However, there are also quantum tasks that display a quantum advantage without entanglement. Distinguishing classical and quantum correlations in quantum systems is therefore of both practical and fundamental importance. Realistic quantum systems are not closed, and therefore it is important to study the various correlations when the system loses its coherence due to interactions with the environment. In this paper, we study in detail the dynamics of different kinds of correlations, classical correlation, quantum discord and entanglement in open quantum systems, in particular, a two-qubit system evolving under Kossakowski-type quantum dynamical semigroups of completely positive maps. In such an environment, classical and quantum correlations can even persist asymptotically. By analytic and numerical analysis, we find that the quantum discord is larger than the classical correlation for asymptotic states. Furthermore, we show that the quantum discord is more resistant to the action of the environment than quantum entanglement, and it can persist even in the asymptotic long-time regime.

Is Branching Intensity Interspecifically Related to Biomass Allocation? A Survey of 25 Dicot Shrub Species from an Open‐Growing Dry Valley

The objective of this study was to test whether branching intensity is interspecifically correlated with the biomass allocation patterns of woody species at the level of the whole plant. For this purpose, we examined leaf size and number and branch size and number at different branch orders and computed both a commonly used measure and a newly constructed measure of branching intensity (i.e., Whitney’s parameter and γ, respectively) to determine whether biomass allocation patterns are correlated with branching intensity for 25 shrub species from a dry valley in southwest China. Whitney’s parameter (BI) was calculated as $$( N_{\mathrm{T}\,}-1) / ( N_{\mathrm{T}\,}-N_{\mathrm{t}\,}) $$ for whole plants, where NT is the total branch number at different branch orders and Nt is the number of terminal branches. Gamma was calculated as Nt divided by the maximum branch order. No significant across‐species relationship was found between BI and the quotient of leaf and stem mass. However, a positive correlation was observed between BI and the quotient of stem and root mass. In contrast, γ was negatively correlated with the quotient of leaf and stem mass but not correlated with the quotient of stem and root mass. The relationship between branching intensity and biomass allocation patterns could be understood from the allometries among the study architectural traits. In conclusion, branching intensity is interspecifically correlated with biomass allocation patterns. However, the correlation is parameter specific, because different measures of branching intensity produce different kinds of correlations.

Monogamy of correlations versus monogamy of entanglement

A fruitful way of studying physical theories is via the question whether the possible physical states and different kinds of correlations in each theory can be shared to different parties. Over the past few years it has become clear that both quantum entanglement and non-locality (i.e., correlations that violate Bell-type inequalities) have limited shareability properties and can sometimes even be monogamous. We give a self-contained review of these results and present new results on the shareability of different kinds of correlations, including local, quantum and no-signalling correlations. This includes an alternative simpler proof of the Toner-Verstraete monogamy inequality for quantum correlations, as well as a strengthening thereof. Further, the relationship between sharing non-local quantum correlations and sharing mixed entangled states is investigated, and already for the simplest case of bi-partite correlations and qubits this is shown to be non-trivial. Also, a recently proposed new interpretation of Bell’s theorem by Schumacher in terms of shareability of correlations is critically assessed. Finally, the relevance of monogamy of non-local correlations for secure quantum key distribution is pointed out, and in this regard it is stressed that not all non-local correlations are monogamous.

Flow unit modeling and fine-scale predicted permeability validation in Atokan sandstones: Norcan East field, Kansas

Characterizing the reservoir interval into flow units is an effective way to subdivide the net-pay zone into layers for reservoir simulation. Commonly used flow unit identification techniques require a reliable estimate of permeability in the net pay on a foot-by-foot basis. Most of the wells do not have cores, and the literature is replete with different kinds of correlations, transforms, and prediction methods for profiling permeability in pay. However, for robust flow unit determination, predicted permeability at noncored wells requires validation and, if necessary, refinement. This study outlines the use of a spreadsheet-based permeability validation technique to characterize flow units in wells from the Norcan East field, Clark County, Kansas, that produce from Atokan aged fine- to very fine-grained quartzarenite sandstones interpreted to have been deposited in brackish-water, tidally dominated restricted tidal-flat, tidal-channel, tidal-bar, and estuary bay environments within a small incised-valley-fill system. The methodology outlined enables the identification of fieldwide free-water level and validates and refines predicted permeability at 0.5-ft (0.15-m) intervals by iteratively reconciling differences in water saturation calculated from wire-line log and a capillary-pressure formulation that models fine- to very fine-grained sandstone with diagenetic clay and silt or shale laminae. The effectiveness of this methodology was confirmed by successfully matching primary and secondary production histories using a flow unit-based reservoir model of the Norcan East field without permeability modifications. The methodologies discussed should prove useful for robust flow unit characterization of different kinds of reservoirs.

Correlation Effects in Disordered Metallic Photonic Crystal Slabs

We analyze the influence of correlations on the optical properties of disordered metallic photonic crystal slabs experimentally and theoretically. Different disorder models with different nearest-neighbor correlations are considered. We present a theory that allows us to quantitatively calculate the optical properties of the different samples. We find that different kinds of correlations produce characteristic spectral features such as peak reduction and inhomogeneous broadening. These features are caused by reduced excitation efficiencies and the excitation of multiple resonances.

Development of Novel Statistical Potentials Describing Cation−π Interactions in Proteins and Comparison with Semiempirical and Quantum Chemistry Approaches

Novel statistical potentials derived from known protein structures are presented. They are designed to describe cation-pi and amino-pi interactions between a positively charged amino acid or an amino acid carrying a partially charged amino group and an aromatic moiety. These potentials are based on the propensity of residue types to be separated by a certain spatial distance or to have a given relative orientation. Several such potentials, describing different kinds of correlations between residue types, distances, and orientations, are derived and combined in a way that maximizes their information content and minimizes their redundancy. To test the ability of these potentials to describe cation-pi and amino-pi systems, we compare their energies with those computed with the CHARMM molecular mechanics force field and with quantum chemistry calculations at the Hartree-Fock level (HF) and at the second order of the Møller-Plesset perturbation theory (MP2). The latter calculations are performed in the gas phase and in acetone, in order to mimic the average dielectric constant of protein environments. The energies computed with the best of our statistical potentials and with gas-phase HF or MP2 show correlation coefficients up to 0.96 when considering one side-chain degree of freedom in the statistical potentials and up to 0.94 when using a totally simplified model excluding all side-chain degrees of freedom. These potentials perform as well as, or better than, the CHARMM molecular mechanics force field that uses a much more detailed protein representation. The good performance of our cation-pi statistical potentials suggests their utility in protein structure and stability prediction and in protein design.

The absence of localization in one-dimensional disordered harmonic chains

We study one-dimensional harmonic chains in which clusters of two or three defect atoms are embedded randomly. The disorder in the systems appears in the masses of the atoms. Reflectionless modes are obtained by studying different kinds of correlation among the masses. The localization behaviour of the modes around these special frequencies is examined analytically as well as numerically. To discern the nature of the modes at and around those frequencies, density of states, bandwidth scaling and site Green functions are studied. If the special frequencies lie within the common band of the constituent atoms and at zero the modes are extended at and around them. However, the modes are critical when the special frequency appears at the upper band edge of the host system. The number of non-scattered modes is estimated for all cases. It is approximately square root N for the dimer problem. For the trimer problem with degenerate resonances appearing inside the constituent band it is approximately N34 /. If the degenerate resonances of the trimer appear at zero frequency the number of non-scattered modes is approximately N56/.

Origin of spin polarization and magnetic dichroism in core-level photoemission.

Spin polarization and magnetic circular and linear dichroism in photoemission are interpreted in a many-electron approach. The six different ways to orient the three polarizations in the experiment (magnetization, electric vector of the light, and spin of the photoelectron) allow measurement of six different kinds of correlation between the corresponding atomic properties (valance spin, core-hole orbital momentum, and core-hole spin, respectively). This allows us to analyze exchange and hybridization effects and is illustrated for the 2p and 3p photoemission of ferromagnetic Ni metal.