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Entanglement is fundamental inasmuch because it rephrases the quest for the classical-quantum demarcation line, and it also has potentially enormous practical applications in modern information technology. In this work, employing the approach of matrix decomposition, we introduce and formulate a practicable criterion for separability based on the correlation tensor. It is interesting that this criterion unifies several relevant separability criteria proposed before, even stronger than some of them. Theoretical analysis and detailed examples demonstrate its availability and feasibility for entanglement detection. Furthermore we build a family of entanglement witnesses using the criterion according to its linearity in the density operator space. [ABSTRACT FROM AUTHOR]

As one of the most profound features of quantum mechanics, entanglement is a vital resource for quantum information processing. Inspired by the recent work on PT-moments and separability [Phys. Rev. Lett. 127, 060504 (2021)], we propose two sets of separability criteria using moments of the correlation tensor for bipartite and multipartite quantum states, which are shown to be stronger in some aspects in detecting entanglement. [ABSTRACT FROM AUTHOR]

We study the genuine multipartite entanglement of arbitrary n-partite quantum states by representing the density matrices in terms of the generalized Pauli operators. We introduce a general framework for detecting genuine multipartite entanglement and non full-separability of multipartite quantum states with arbitrary dimensions based on correlation tensors. Effective criterion is derived to verify the genuine multipartite entanglement. Detailed examples are given to show that the criterion detects more genuine multipartite entanglement than the existing criteria.

We study detection of genuine multipartite entanglement based on one-particle loss operator. We obtain a criterion on detecting genuine pure tripartite entanglement. The results are then generalized to arbitrary pure multipartite states. For mixed states by using the correlation tensors of the Bloch representation of density matrices, we obtain an effective criterion of arbitrary dimensional genuine tripartite entanglement. Detailed examples are given to show that our criterion is able to detect more genuine tripartite entanglement states than some existing criteria. [ABSTRACT FROM AUTHOR]

When an n-partite physical system is measured by n observers, the joint probabilities of outcomes conditioned on the observables chosen by the n- parties form a nonnegative tensor P, called an n-partite correlation tensor (CT). According to the special relativity, CTs can be classified as signaling and nonsignaling ones; and from the point of view of hidden variable theory, CTs can be divided into Bell local and Bell nonlocal ones. In this paper, we aim to establish some Bell bi-inequalities for n-partite Bell local correlation tensors. A Bell bi-inequality consists of two Bell inequalities that hold only for Bell local CTs. First, we obtain an inequality for n-partite nonsignaling CTs, which can be used to check the nonsignaling property of a CT. Second, we recall the mathematical definition of Bell locality of CTs and prove global properties of the set of all Bell local CTs over an index set Δn. Then we establish a series tight Bell bi-inequalities and prove that a CT P is Bell local if and only if it satisfies all tight Bell bi-inequalities. Lastly, we list some examples to illustrate how to establish a Bell bi-inequality. [ABSTRACT FROM AUTHOR]

In this work, we discuss two types of trilocality of probability tensors (PTs) P = 〚 P (a 1 a 2 a 3) 〛 over an outcome set Ω 3 and correlation tensors (CTs) P = 〚 P (a 1 a 2 a 3 | x 1 x 2 x 3) 〛 over an outcome-input set Δ 3 based on a triangle network and described by continuous (integral) and discrete (sum) trilocal hidden variable models (C-triLHVMs and D-triLHVMs). We say that a PT (or CT) P is C-trilocal (resp. D-trilocal) if it can be described by a C-triLHVM (resp. D-triLHVM). It is proved that a PT (resp. CT) is D-trilocal if and only if it can be realized in a triangle network by three shared separable states and a local POVM (resp. a set of local POVMs) performed at each node; a CT is C-trilocal (resp. D-trilocal) if and only if it can be written as a convex combination of the product deterministic CTs with a C-trilocal (resp. D-trilocal) PT as a coefficient tensor. Some properties of the sets consisting of C-trilocal and D-trilocal PTs (resp. C-trilocal and D-trilocal CTs) are proved, including their path-connectedness and partial star-convexity. [ABSTRACT FROM AUTHOR]

We revisit the genuine multipartite entanglement by a simplified method, which only involves the Schmidt decomposition and local unitary transformation. We construct a local unitary equivalent class of the tri-qubit quantum state, then use the trace norm of the whole correlation tensor as a measurement to detect genuine multipartite entanglement. By detailed examples, we show our result can detect more genuinely entangled states. Furthermore, we generalize the genuine multipartite entanglement criterion to tripartite higher-dimensional systems. [ABSTRACT FROM AUTHOR]

We study genuine multipartite entanglement of arbitrary n-partite quantum states by representing the density matrices in terms of generalized Pauli operators. While the usual Bloch representation of a density matrix uses three types of generators in the special unitary Lie algebra su (d) , the Weyl representation with generalized Pauli operators has one uniformed type of generators that simplifies computation. In this paper, we take the advantage of this simplicity to derive useful and operational criteria to detect genuine tripartite entanglement. We also generalize the results to obtain a sufficient criterion to detect genuine entanglement for multipartite quantum states in arbitrary dimensions. The new method can detect more genuine entangled states than previous methods as backed by detailed examples. [ABSTRACT FROM AUTHOR]

By exploiting the high-dimensional probability tensor, Li and Qiao (Quantum Inf Process 20:109, 2021) proposed quantum magic square (QMS) models to characterize the diverse forms of nonlocal phenomena and derived a conditional majorization uncertainty relation to witness quantum steering. Motivated by this work, we propose the concepts of the probability and operator QMSs (P-QMSs and O-QMSs) to characterize Bell nonlocality of a bipartite correlation tensor (BCT) and EPR steerability of a bipartite state. We prove that a BCT is Bell local if and only if it has a P-QMS for Alice or a P-QMS for Bob and a bipartite state shared by Alice and Bob is one-way unsteerable with a measurement assemblage of Alice if and only if it has an O-QMS. [ABSTRACT FROM AUTHOR]

Turbulent flows play a major role in many fields of science and industry. Noticeable attention is seen on turbulent flows of suspending fibers because of the sensitivity of the electrical, thermal, and mechanical properties of the connecting fiber composites to the spatial configuration and orientation of fibers. The involvement of fibers in the turbulent flow greatly affects the turbulent energy. It is more influenced when the turbulent flow occurs in a rotating system. The effect of fibers on the turbulent energy in the rotating frame must therefore be investigated. For turbulent energy with fiber suspension, a mathematical model can be built in a rotating system that is very important to enhance the quality of industrial goods. This paper, therefore, develops a mathematical model for turbulent energy motion in a rotating frame with a fiber suspension. The model was formulated using the averaging procedure. The momentum equation for incompressible and viscous fluid turbulent flow was considered to develop the model. The turbulent energy motion of the fiber suspensions was presented in the rotating frame in second-order correlation tensors,Wi,j,Si,j,Li,j,Fi,j,Gi,j,Di,j,Qi,j, andHi,j, where all the tensors are the function of time, distance, and space coordinates.

We study entanglement and genuine entanglement of tripartite and four-partite quantum states by using Heisenberg-Weyl (HW) representation of density matrices. Based on the correlation tensors in HW representation, we present criteria to detect entanglement and genuine tripartite and four-partite entanglement. Detailed examples show that our method can detect more entangled states than previous criteria. [ABSTRACT FROM AUTHOR]

When an n-partite physical system is measured by n observers, the joint probabilities of outcomes conditioned on the observables chosen by the n parties form a nonnegative tensor, called an n-partite correlation tensor (CT). In this paper, we aim to establish some characterizations of nonsignaling and Bell locality of an n-partite CT, respectively. By placing CTs within the linear space of correlation-type tensors (CTTs), we prove that every n-partite nonsignaling CTT can be decomposed as a linear combination of all local deterministic CTs using single-value decomposition of matrices and mathematical induction. As a consequence, we prove that an n-partite CT is nonsignaling (resp. Bell local) if and only if it can be written as a quasi-convex (resp. convex) combination of the outer products of deterministic CTs, implying that an n-partite CT is nonsignaling if and only if it has a local hidden variable model governed by a quasi-probability distribution. As an application of these results, we prove that a CT is nonsignaling if and only if it can be written as a quasi-convex of two Bell local ones, revealing a close relationship between nonsignaling CTs and Bell local ones.

In this paper, we investigate the genuine entanglement in tripartite systems based on partial transposition and the norm of correlation tensors of the density matrices. We first derive an analytical sufficient criterion to detect genuine entanglement of tripartite qubit states combining with the partial transposition of the density matrices. Then, we use the norm of correlation tensors to study genuine entanglement for tripartite qudit quantum states and obtain a genuine entanglement criterion by constructing certain matrices. With detailed examples, our results are seen to be able to detect more genuine tripartite entangled states than previous studies. [ABSTRACT FROM AUTHOR]

We study the genuine multipartite entanglement in tripartite quantum systems. By using the Schmidt decomposition and local unitary transformation, we convert the general states to simpler forms and consider certain matrices from correlation tensors in the Bloch representation of the simplified density matrices. Using these special matrices, we obtain new criteria for genuine multipartite entanglement. Detail examples show that our criteria are able to detect more tripartite entangled and genuine tripartite entangled states than some existing criteria. [ABSTRACT FROM AUTHOR]

Turbulent flows play a major role in many fields of science and industry. Noticeable attention is seen on turbulent flows of suspending fibers because of the sensitivity of the electrical, thermal, and mechanical properties of the connecting fiber composites to the spatial configuration and orientation of fibers. The involvement of fibers in the turbulent flow greatly affects the turbulent energy. It is more influenced when the turbulent flow occurs in a rotating system. The effect of fibers on the turbulent energy in the rotating frame must therefore be investigated. For turbulent energy with fiber suspension, a mathematical model can be built in a rotating system that is very important to enhance the quality of industrial goods. This paper, therefore, develops a mathematical model for turbulent energy motion in a rotating frame with a fiber suspension. The model was formulated using the averaging procedure. The momentum equation for incompressible and viscous fluid turbulent flow was considered to develop the model. The turbulent energy motion of the fiber suspensions was presented in the rotating frame in second-order correlation tensors, W i , j , S i , j , L i , j , F i , j , G i , j , D i , j , Q i , j , and H i , j , where all the tensors are the function of time, distance, and space coordinates. [ABSTRACT FROM AUTHOR]

The emergence of cryptoassets has sparked a paradigm shift in the world of finance and investment, ushering in a new era of digital assets with profound implications for the future of currency and asset management. A recent study showed that during the bubble period around the year, 2018, the price of cryptoasset, XRP has a strong anti correlation with the largest singular values of the correlation tensors obtained from the weekly XRP transaction networks. In this study, we provide a detailed analysis of the method of correlation tensor spectra for XRP transaction networks. We calculate and compare the distribution of the largest singular values of the correlation tensor using the random matrix theory with the largest singular values of the empirical correlation tensor. We investigate the correlation between the XRP price and the largest singular values for a period spanning two years. We also uncover the distinct dependence between the XRP price and the singular values for bubble and non-bubble periods. The significance of the time evolution of singular values is shown by comparison with the evolution of singular values of the reshuffled correlation tensor. Furthermore, we identify a set of driver nodes in the transaction networks that drives the market during the bubble period using singular vectors. • Correlation tensor spectra reveal distinctive patterns in XRP transaction networks. • Showcasing significance of singular values with Random Matrix Theory. • Largest singular values anti-correlated with XRP price during the bubble periods. • Singular vectors identify key driver nodes impacting the market. [ABSTRACT FROM AUTHOR]

We investigate genuine multipartite entanglement in general multipartite systems. Based on the norms of the correlation tensors of a multipartite state under various partitions, we present an analytical and sufficient criterion for detecting the genuine four-partite entanglement. The results are generalized to arbitrary multipartite systems. [ABSTRACT FROM AUTHOR]

We study the genuine multipartite entanglement of arbitrary n -partite quantum states by representing the density matrices in terms of the generalized Pauli operators. We introduce a general framework for detecting genuine multipartite entanglement and non full-separability of multipartite quantum states with arbitrary dimensions based on correlation tensors. Effective criterion is derived to verify the genuine multipartite entanglement. Detailed examples are given to show that the criterion detects more genuine multipartite entanglement than the existing criteria. [ABSTRACT FROM AUTHOR]

Noise affects production and transmission of entanglement. We use a handy approach for a noise resistance of entanglement of two-qudit systems. A geometric concept using correlation tensors of separable and entangled states is implemented to formulate entanglement criterion. We apply the criterion to the various types of noise (white, colored, local depolarizing and amplitude damping) admixtures with the initial (pure) state. We also study the noise resistance with respect to the violation of specific family of Bell inequalities (CGLMP). A broad set of numerical and analytical results is presented. [ABSTRACT FROM AUTHOR]