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The multipartite nonlocality provides deep insights into the fundamental feature of quantum mechanics and guarantees different degrees of cryptography security for potential applications in the quantum internet. Verifying multipartite nonlocal correlations is a difficult task. A unified approach is proposed that encompasses all the quantum characteristics of the multipartite correlated system beyond from fully separable to biseparable no‐signaling correlations. A straightforward method is offered to verify general systems by lifting partial nonlocal correlations. This allows to construct a chained Bell inequality, facilitating the unified verification of hierarchic multipartite nonlocalities. The lifting method is finally applied to verify the correlations derived from quantum networks. [ABSTRACT FROM AUTHOR]

Quantum entanglement plays a key role in quantum computation and quantum information processing. It is of great significance to find efficient and experimentally friend separability criteria to detect entanglement. In this paper, we firstly propose two easily used entanglement criteria based on matrix moments. The first entanglement criterion only uses the first two realignment moments of a density matrix. The second entanglement criterion is based on the moments related to the partially transposed matrix. By detailed examples we illustrate the effectiveness of these criteria in detecting entanglement. Moreover, we provide an experimentally measurable lower bound of concurrence based on these moments. Finally, we present both bipartite and genuine tripartite entanglement measures based on the moments of the reduced states. By detailed examples, we show that our entanglement measures characterize the quantum entanglement in a more fine ways than the existing measures. [ABSTRACT FROM AUTHOR]

The monogamy property of entanglement is an intriguing feature of multipartite quantum entanglement. Most entanglement measures satisfying the monogamy inequality have turned out to be convex. Whether nonconvex entanglement measures obey the monogamy inequalities remains less known at present. As a well-known measure of entanglement, the logarithmic negativity is not convex. We elucidate the constraints of multi-qubit entanglement based on the logarithmic convex-roof extended negativity (LCREN) and the logarithmic convex-roof extended negativity of assistance (LCRENoA). Using the Hamming weight derived from the binary vector associated with the distribution of subsystems, we establish monogamy inequalities for multi-qubit entanglement in terms of the α th-power ( α ≥ 4 ln 2 ) of LCREN, and polygamy inequalities utilizing the α th-power ( 0 ≤ α ≤ 2 ) of LCRENoA. We demonstrate that these inequalities give rise to tighter constraints than the existing ones. Furthermore, our monogamy inequalities are shown to remain valid for the high-dimensional states that violate the CKW monogamy inequality. Detailed examples are presented to illustrate the effectiveness of our results in characterizing the multipartite entanglement distributions. [ABSTRACT FROM AUTHOR]

This study provides a generalized definition of polygamy relations for any quantum correlation measures. Instead of the usual polygamy inequality, a polygamy relation with equality is given by introducing the polygamy weight. From the polygamy relation with equality, it presents polygamy inequalities satisfied by the βth (β>0)$(\beta >0)$ power of the quantum correlation measures. Taking concurrence of assistance as an example, it further illustrates the significance and advantages of these relations. It also obtains a polygamy relation with equality by considering the one‐to‐group entanglements for any quantum entanglement measures that do not satisfy the polygamy relations. It demonstrates that such relations for tripartite states can be generalized to multipartite systems. [ABSTRACT FROM AUTHOR]

Originated from the work extraction in quantum systems coupled to a heat bath, quantum deficit is a kind of significant quantum correlations like quantum entanglement. It links quantum thermodynamics with quantum information. We analytically calculate the one-way deficit of the generalized n-qubit Werner state. We find that the one-way deficit increases as the mixing probability p increases for any n. For fixed p, we observe that the one-way deficit increases as n increases. For any n, the maximum of one-way deficit is attained at p = 1 . Furthermore, for large n ( 2 n → ∞ ), we prove that the curve of one-way deficit versus p approaches to a straight line with slope 1. We also calculate the Holevo quantity for the generalized n-qubit Werner state and show that it is zero. [ABSTRACT FROM AUTHOR]

The entanglement in multipartite quantum system is hard to characterize and quantify, although it has been intensively studied in bipartite systems. The monogamy of entanglement, as a special property of multipartite systems, shows the distribution of entanglement in the system. In this paper, we investigate the monogamy relations for multi-qubit systems. By using two entangled measures, namely the concurrence C and the negativity N c , we establish tighter monogamy inequalities for their α -th power than those in all the existing ones. We also illustrate the tightness of our results for some classes of quantum states. [ABSTRACT FROM AUTHOR]

Multipartite entanglement is of important resources for quantum communication and quantum computation. The goal of this paper is to characterize general multipartite entangled states according to shallow quantum circuits. It is first proved that any genuinely multipartite entanglement on finite‐dimensional spaces can be generated by using 2‐layer shallow quantum circuit consisting of two biseparable quantum channels, which has the smallest nontrivial circuit depth in the shallow quantum circuit model. Further, a semi‐device‐independent entanglement model depending on the local connection ability in the second layer of quantum circuits is proposed. This implies a complete hierarchy of distinguishing genuinely multipartite entangled states. It shows a completely different multipartite nonlocality from the quantum network entanglement. These results show new insights for the multipartite entanglement, quantum network, and measurement‐based quantum computation. [ABSTRACT FROM AUTHOR]

Einstein-Podolsky-Rosen steering is a kind of powerful nonlocal quantum resource in quantum information processing such as quantum cryptography and quantum communication. Many criteria have been proposed in the past few years to detect steerability, both analytically and numerically, for bipartite quantum systems. We propose effective criteria for tripartite steerability and genuine tripartite steerability of three-qubit quantum states by establishing connections between the tripartite steerability (resp. genuine tripartite steerability) and the tripartite entanglement (resp. genuine tripartite entanglement) of certain corresponding quantum states. From these connections, tripartite steerability and genuine tripartite steerability can be detected without using any steering inequalities. The "complex cost" of determining tripartite steering and genuine tripartite steering can be reduced by detecting the entanglement of the newly constructed states in the experiment. Detailed examples are given to illustrate the power of our criteria in detecting the (genuine) tripartite steerability of tripartite states. [ABSTRACT FROM AUTHOR]

Uncertainty relation is a fundamental issue in quantum mechanics and quantum information theory. By using modified generalized variance (MGV), and modified generalized Wigner–Yanase–Dyson skew information (MGWYD), we identify the total and quantum uncertainty of quantum channels. The elegant properties of the total uncertainty of quantum channels are explored in detail. In addition, we present a trade-off relation between the total uncertainty of quantum channels and the entanglement fidelity and establish the relationships between the total uncertainty and entropy exchange/coherent information. Detailed examples are given to the explicit formulas of the total uncertainty and the quantum uncertainty of quantum channels. Moreover, utilizing a realizable experimental measurement scheme by using the Mach–Zehnder interferometer proposed in Nirala et al. (Phys Rev A 99:022111, 2019), we discuss how to measure the total/quantum uncertainty of quantum channels for pure states. [ABSTRACT FROM AUTHOR]

We propose a novel parameterized entanglement measure α -concurrence for bipartite systems. By employing positive partial transposition and realignment criteria, we derive analytical lower bounds for the α -concurrence. Moreover, we calculate explicitly the analytic expressions of the α -concurrence for isotropic states and Werner states. [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]

We investigate the monogamy relations related to the concurrence, the entanglement of formation, convex-roof extended negativity, Tsallis-q entanglement and Rényi-α entanglement, the polygamy relations related to the entanglement of formation, Tsallis-q entanglement and Rényi-α entanglement. Monogamy and polygamy inequalities are obtained for arbitrary multipartite qubit systems, which are proved to be tighter than the existing ones. Detailed examples are presented. [ABSTRACT FROM AUTHOR]

We study the detection of multipartite entanglement based on the generalized local uncertainty relations. A sufficient criterion for the entanglement of four-partite quantum systems is presented in terms of the local uncertainty relations. Detailed examples are given to illustrate the advantages of our criterion. The approach is generalized to general multipartite entanglement cases. [ABSTRACT FROM AUTHOR]

Genuine multipartite entanglement plays important roles in quantum information processing. The detection of genuine multipartite entanglement has been long time a challenging problem in the theory of quantum entanglement. We propose a criterion for detecting genuine tripartite entanglement of arbitrary dimensional tripartite states based on quantum Fisher information. We show that this criterion is more effective for some states in detecting genuine tripartite entanglement by detailed example. [ABSTRACT FROM AUTHOR]

Quantum entanglement plays essential roles in quantum information processing. The monogamy and polygamy relations characterize the entanglement distributions in the multipartite systems. We present a class of monogamy inequalities related to the μ-th power of the entanglement measure based on Rényi-α entropy, as well as polygamy relations in terms of the μ-th power of Rényi-α entanglement of assistance. These monogamy and polygamy relations are shown to be tighter than the existing ones. [ABSTRACT FROM AUTHOR]

Quantum entanglement plays significant roles in quantum information processing. Estimating quantum entanglement is an essential and difficult problem in the theory of quantum entanglement. We study two main measures of quantum entanglement: concurrence and convex-roof extended negativity. Based on the improved separability criterion from the Bloch representation of density matrices, we derive analytical lower bounds of the concurrence and the convex-roof extended negativity for arbitrary dimensional bipartite quantum systems. We show that these bounds are better than some of the existing ones by detailed examples. [ABSTRACT FROM AUTHOR]

We study the trade-off relations given by the l 1 -norm coherence of general multipartite states. Explicit trade-off inequalities are derived with lower bounds given by the coherence of either bipartite or multipartite reduced density matrices. In particular, for pure three-qubit states, it is explicitly shown that the trade-off inequality is lower bounded by the three tangle of quantum entanglement. [ABSTRACT FROM AUTHOR]

We study the properties of coherence concurrence and present a physical explanation analogous to the coherence of assistance. We give an optimal pure state decomposition which attains the coherence concurrence for qubit states. We prove the additivity of coherence concurrence under direct sum operations in another way. Using these results, we calculate analytically the coherence concurrence for X states and show its optimal pure state decompositions. Moreover, we show that the coherence concurrence is exactly twice the convex roof-extended negativity of the Schmidt correlated states, thus establishing a direct relation between coherence concurrence and quantum entanglement. [ABSTRACT FROM AUTHOR]

We investigate the generalized monogamy and polygamy relations N-qubit systems. We give a general upper bound of the αth (0 ≤ α ≤ 2) power of concurrence for N-qubit states. The monogamy relations satisfied by the αth (0 ≤ α ≤ 2) power of concurrence are presented for N-qubit pure states under the partition AB and C1...CN− 2, as well as under the partition ABC1 and C2⋯CN− 2. These inequalities give rise to the restrictions on entanglement distribution and the trade off of entanglement among the subsystems. Similar results are also derived for negativity. [ABSTRACT FROM AUTHOR]

We investigate polygamy relations of multipartite entanglement in arbitrary-dimensional quantum systems. By improving an inequality and using the βth (0 ≤ β ≤ 1) power of entanglement of assistance, we provide a new class of weighted polygamy inequalities of multipartite entanglement in arbitrary-dimensional quantum systems. We show that these new polygamy relations are tighter than the ones given in Kim (Phys. Rev. A 97, 042332 2018). [ABSTRACT FROM AUTHOR]

We investigate the quantum phase transitions for the spin-1/2 chains via the quantum correlations between the nearest and next-to-nearest neighbor spins characterized by negativity, information deficit, trace distance discord and local quantum uncertainty. It is shown that all these correlations exhibit the quantum phase transitions at . However, only information deficit and local quantum uncertainty can demonstrate quantum phase transitions at . The analytical and numerical behaviors of the quantum correlations for the system are presented. We also consider quantum correlations in the Hartree-Fock ground state of the Lipkin-Meshkov-Glick (LMG) model. [ABSTRACT FROM AUTHOR]

We generalize the notion of unextendible maximally entangled basis from bipartite systems to multipartite quantum systems. It is proved that there do not exist unextendible maximally entangled bases in three-qubit systems. Moreover, two types of unextendible maximally entangled bases are constructed in tripartite quantum systems and proved to be not mutually unbiased. [ABSTRACT FROM AUTHOR]

We present an analytical lower bound of multipartite concurrence based on the generalized Bloch representations of density matrices. It is shown that the lower bound can be used as an effective entanglement witness of genuine multipartite entanglement. Tight lower and upper bounds for multipartite tangles are also derived. Since the lower bounds depend on just part of the correlation tensors, the result is experimentally feasible. [ABSTRACT FROM AUTHOR]

We investigate one-way quantum deficit for 2 ⊗ d systems. Analytical expressions of one-way quantum deficit under both von Neumann measurement and weak measurement are presented. As an illustration, qubit-qutrit systems are studied in detail. It is shown that there exists non-zero one-way quantum deficit even quantum entanglement vanishes. Moreover, one-way quantum deficit via weak measurement turns out to be weaker than that via von Neumann measurement. The dynamics of entanglement and one-way quantum deficit under dephasing channels is also investigated. [ABSTRACT FROM AUTHOR]

We present several criteria for genuine multipartite entanglement from universal uncertainty relations based on majorization theory. Under non-negative Schur-concave functions, the vector-type uncertainty relation generates a family of infinitely many detectors to check genuine multipartite entanglement. We also introduce the concept of k-separable circles via geometric distance for probability vectors, which include at most ( k−1)-separable states. The entanglement witness is also generalized to a universal entanglement witness which is able to detect the k-separable states more accurately. [ABSTRACT FROM AUTHOR]

We study sum uncertainty relations for arbitrary finite N quantum mechanical observables. Some uncertainty inequalities are presented by using skew information introduced by Wigner and Yanase. These uncertainty inequalities are nontrivial as long as the observables are mutually noncommutative. The relations among these new and existing uncertainty inequalities have been investigated. Detailed examples are presented. [ABSTRACT FROM AUTHOR]

In this paper, we study the one-way local operations and classical communication (LOCC) problem. In $$\mathbb {C}^d\otimes \mathbb {C}^d$$ with $$d\ge 4$$ , we construct a set of $$3\lceil \sqrt{d}\rceil -1$$ one-way LOCC indistinguishable maximally entangled states which are generalized Bell states. Moreover, we show that there are four maximally entangled states which cannot be perfectly distinguished by one-way LOCC measurements for any dimension $$d\ge 4$$ . [ABSTRACT FROM AUTHOR]

The mutually unbiasedness between a maximally entangled basis (MEB) and an unextendible maximally entangled system (UMES) in the bipartite system $\mathbb {C}^{2}\otimes \mathbb {C}^{2^{k}} (k>1)$ are introduced and discussed first in this paper. Then two mutually unbiased pairs of a maximally entangled basis and an unextendible maximally entangled system are constructed; lastly, explicit constructions are obtained for mutually unbiased MEB and UMES in $\mathbb {C}^{2}\otimes \mathbb {C}^{4}$ and $\mathbb {C}^{2}\otimes \mathbb {C}^{8}$, respectively. [ABSTRACT FROM AUTHOR]

We study the quantum separability problem by using general symmetric informationally complete measurements and present separability criteria for both $$d$$ -dimensional bipartite and multipartite systems. The criterion for bipartite quantum states is effective in detecting several well-known classes of quantum states. For isotropic states, it becomes both necessary and sufficient. Furthermore, our criteria can be experimentally implemented, and the criterion for two-qudit states requires less local measurements than the one based on mutually unbiased measurements. [ABSTRACT FROM AUTHOR]

We study maximally entangled bases in bipartite systems $$\mathbb {C}^d \otimes \mathbb {C}^{kd}\ (k\in Z^{+})$$ , which are mutually unbiased. By systematically constructing maximally entangled bases, we present an approach in constructing mutually unbiased maximally entangled bases. In particular, five maximally entangled bases in $$\mathbb {C}^2 \otimes \mathbb {C}^{4}$$ and three maximally entangled bases in $$\mathbb {C}^2 \otimes \mathbb {C}^{6}$$ that are mutually unbiased are presented. [ABSTRACT FROM AUTHOR]

In this paper, we give a method for the local unitary equivalent problem which is more efficient than that was proposed by Bin Liu et al []. [ABSTRACT FROM AUTHOR]

We systematically study the construction of mutually unbiased bases in $\mathbb {C}^{2}\bigotimes \mathbb {C}^{3}$, such that all the bases are unextendible maximally entangled ones. Necessary conditions of constructing a pair of mutually unbiased unextendible maximally entangled bases in $\mathbb {C}^{2}\bigotimes \mathbb {C}^{3}$ are derived. Explicit examples are presented. [ABSTRACT FROM AUTHOR]

Based on the generators of SU(n) we present inequalities for detecting quantum entanglement for 2 ⊗ d and M ⊗ N systems. These inequalities provide a sufficient condition of entanglement for bipartite mixed states and give rise to an experimental way of entanglement detection. [ABSTRACT FROM AUTHOR]

We study the concurrence of four-qubit quantum states and provide analytical lower bounds of concurrence in terms of the monogamy inequality of concurrence for qubit systems. It is shown that these lower bounds are able to improve the existing bounds and detect entanglement better. The approach is generalized to arbitrary qubit systems. [ABSTRACT FROM AUTHOR]

We study the stability of NPT property of an arbitrary pure entangled state under the mixture of arbitrary pure separable states. For bipartite pure states with Schmidt number n ( n>1) which is NPT, we show that this state is still NPT when it is mixed with no more than $\frac {n(n-1)}{2}-1$ arbitrary pure separable states. This result is generalized to multipartite case. [ABSTRACT FROM AUTHOR]