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We present a different kind of monogamous relations based on concurrence and concurrence of assistance. For A-qubit systems ABC1... CN-2, the monogamy relations satisfied by the concurrence of N-qubit pure states under the partition AB and C1 ... CN-2, as well as under the partition ABC1, and C2 ... CN-2, are established, which gives rise to a kind of restrictions on the entanglement distribution and trade off among the subsystems. [ABSTRACT FROM AUTHOR]

We investigate the nonlocality distributions among multiqubit systems based on the maximal violations of the Clauser-Horne-Shimony-Holt (CHSH) inequality of reduced pairwise qubit systems. We present a trade-off relation satisfied by these maximal violations, which gives rise to restrictions on the distribution of nonlocality among the subqubit systems. For a three-qubit system, it is impossible that all pairs of qubits violate the CHSH inequality, and once a pair of qubits violates the CHSH inequality maximally, the other two pairs of qubits must both obey the CHSH inequality. Detailed examples are given to illustrate the trade-off relations, and the trade-off relations are generalized to arbitrary multiqubit systems. [ABSTRACT FROM AUTHOR]

We present a complete set of local unitary invariants for generic multiqubit systems which gives necessary and sufficient conditions for two states being local unitary equivalent. These invariants are canonical polynomial functions in terms of the generalized Bloch representation of the quantum states. In particular, we prove that there are at most 12 polynomial local unitary invariants for two-qubit states and at most 90 polynomials for three-qubit states. Comparison with Makhlin's 18 local unitary invariants is given for two-qubit systems. [ABSTRACT FROM AUTHOR]

We investigate the monogamy relations related to the concurrence and the entanglement of formation. General monogamy inequalities given by the αth power of concurrence and entanglement of formation are presented for N-qubit states. The monogamy relation for entanglement of assistance is also established. Based on these general monogamy relations, the residual entanglement of concurrence and entanglement of formation are studied. Some relations among the residual entanglement, entanglement of assistance, and three tangle are also presented. [ABSTRACT FROM AUTHOR]

We study an unextendible maximally entangled basis in arbitrary bipartite spaces. A systematic way of constructing a set of d² orthonormal maximally entangled states in Cd ⊗ Cd'(d'/2 < d < d') is provided. The complementary space of the set of these d² orthonormal maximally entangled states contains no maximally entangled states that are orthogonal to all of them. Furthermore, we investigate mutually unbiased bases in which all the bases are unextendible maximally entangled ones. We present two unextendible maximally entangled bases in C ² ⊗ C ³ which are mutually unbiased. [ABSTRACT FROM AUTHOR]

We provide analytical lower and upper bounds for entanglement of formation for bipartite systems, which give a direct relation between the bounds of entanglement of formation and concurrence, and improve the previous results. Detailed examples are presented. [ABSTRACT FROM AUTHOR]

We present a set of Bell inequalities for multiqubit quantum systems. These Bell inequalities are shown to be able to detect multiqubit entanglement better than previous Bell inequalities such as Werner-Wolf-Zukowski- Brukner ones. Computable formulas are presented for calculating the maximal violations of these Bell inequalities for any multiqubit states. [ABSTRACT FROM AUTHOR]

It is shown that the dissonance, a quantum correlation which is equal to quantum discord for separable state, is required for assisted optimal state discrimination. We find that only one side discord is required in the optimal process of assisted state discrimination, while another side discord and entanglement is not necessary. We confirm that the quantum discord, which is asymmetric depending on local measurements, is a resource for assisted state discrimination. With the absence of entanglement, we give the necessary and sufficient condition for vanishing one side discord in assisted state discrimination for a class of d nonorthogonal states. As a by-product, we find that the positive-partial-transposition condition is the necessary and sufficient condition for the separability of a class of 2 × d states. [ABSTRACT FROM AUTHOR]

Entanglement of formation is an important measure of quantum entanglement. We present an experimental way to measure the entanglement of formation for arbitrary dimensional pure states. The measurement only evolves local quantum mechanical observables. [ABSTRACT FROM AUTHOR]

We propose a set of linear quantum entanglement witnesses constituted by local quantum-mechanical observables with each two possible measurement outcomes. These witnesses detect all the entangled resources which give rise to a better fidelity than separable states in quantum teleportation and present both sufficient and necessary conditions in experimentally detecting the useful resources for quantum teleportation [ABSTRACT FROM AUTHOR]

The problems of genuine multipartite entanglement detection and classification are challenging. We show that a multipartite quantum state is genuine multipartite entangled if the multipartite concurrence is larger than certain quantities given by the number and the dimension of the subsystems. This result also provides a classification of various genuine multipartite entanglements. We present a lower bound of the multipartite concurrence in terms of bipartite concurrences. While various operational approaches are available for providing lower bounds of bipartite concurrences, our results give an effective operational way to detect and classify genuine multipartite entanglement. As applications, genuine multipartite entanglement of tripartite systems is analyzed in detail. [ABSTRACT FROM AUTHOR]

We give an explicit construction of d locally indistinguishable, orthogonal maximally entangled states in Cd ⊗ Cd for any d ≥ 4. This gives an answer to the conjecture proposed by Bandyopadhyay et al. [New J. Phys. 13, 123013 (2011)]. [ABSTRACT FROM AUTHOR]

We investigate the unextendible maximally entangled bases (UMEBs) in Cd Cd and present a 30-number UMEB construction in C6 C6. For the higher-dimensional case, we show that for a given A-number UMEB in Cd Cd, there is an N-number, N = (qd)² - (d² - N), UMEB in € N Cqd for any q € N. As an example, for C 12n C12n systems, we show that there are at least two sets of UMEBs which are not equivalent. [ABSTRACT FROM AUTHOR]

We investigate how the genuine multipartite entanglement is distributed among the components of superposed states. Analytical lower and upper bounds for the usual multipartite negativity and the genuine multipartite entanglement negativity are derived. These bounds are shown to be tight by detailed examples. [ABSTRACT FROM AUTHOR]

We study entanglement detection by using mutually unbiased measurements and provide a quantum separability criterion that can be experimentally implemented for arbitrary ¿-dimensional bipartite systems. We show that this criterion is more effective than the criterion based on mutually unbiased bases. For isotropic states our criterion becomes both necessary and sufficient. [ABSTRACT FROM AUTHOR]

We present a computable criterion for completely classifying multiqubit quantum states under local unitary operations. The criterion can be used to detect whether two quantum states in multiqubit systems are locally unitarily equivalent or not. Once a positive answer is obtained, we are further able to compute the corresponding unitary operators precisely. Since the scheme is based on the mean values of some quantum mechanical observables, it supplies an experimental way to judge the local equivalence of quantum states. [ABSTRACT FROM AUTHOR]

We present separability criteria for both bipartite and multipartite quantum states. These criteria include the criteria based on the correlation matrix and its generalized form as special cases. We show by detailed examples that our criteria are more powerful than the positive partial transposition criterion, the realignment criterion, and the criteria based on the correlation matrices. [ABSTRACT FROM AUTHOR]

We study the entanglement of tripartite quantum states and provide analytical lower bounds of concurrence in terms of the concurrence of substates. The lower bound may improve all of the existing lower bounds of concurrence. The approach is generalized to arbitrary dimensional multipartite systems. [ABSTRACT FROM AUTHOR]

The nonlocal properties of arbitrary dimensional bipartite quantum systems are investigated. A complete set of Invariants under local unitary transformations is presented. These invariants give rise to both sufficient and necessary conditions for the equivalence of quantum States under local unitary transformations: two density matrices are locally equivalent if and only if all these invariants have equal values. [ABSTRACT FROM AUTHOR]

We present a lower bound of concurrence for arbitrary-dimensional bipartite quantum states. This lower bound may be used to improve all the known lower bounds of concurrence. Moreover, the lower bound gives rise to an operational sufficient criterion of distillability of quantum entanglement. The significance of our result is illustrated by quantitative evaluation of entanglement for entangled states that fail to be identified by the usual concurrence estimation method and by showing the distillability of mixed states that cannot be recognized by other distillability criteria. [ABSTRACT FROM AUTHOR]

We present a set of inequalities for detecting quantum entanglement of 2⊗d quantum states. For 2⊗2 and 2⊗3 systems, the inequalities give rise to sufficient and necessary separability conditions for both pure and mixed states. For the case of d>3, these inequalities are necessary conditions for separability, which detect all entangled states that are not positive under partial transposition and even some entangled states with positive partial transposition. These inequalities are given by mean values of local observables and present an experimental way of detecting the quantum entanglement of 2⊗d quantum states and even multiqubit pure states. [ABSTRACT FROM AUTHOR]

We study the concurrence of arbitrary dimensional bipartite quantum systems. An explicit analytical lower bound of concurrence is obtained which detects entanglement for some quantum states better than some well-known separability criteria and improves the lower bounds, such as from the positive partial transposition, realignment criteria, and Breuer's entanglement witness. [ABSTRACT FROM AUTHOR]

We study the level surfaces of quantum discord for a class of two-qubit states with parallel nonzero Bloch vectors. The dynamic behavior of quantum discord under decoherence is investigated. It is shown that a class of X states has sudden transition between classical and quantum correlations under decoherence. Our results include the ones in M. D. Lang and C. M. Caves Phys. Rev. Lett. 105 150501 (2010) as a special case and show new pictures and structures of quantum discord. [ABSTRACT FROM AUTHOR]

We study remote creation of coherence (RCC) for a quantum system, A, with the help of quantum operations on another system, B, and one-way classical communication. We show that all the nonincoherent quantum states are useful for RCC and all the incoherent-quantum states are not. The necessary and sufficient conditions of RCC for the quantum operations on system B are presented for pure states. The upper bound of average RCC is derived, giving a relation among the entanglement (concurrence), the RCC of the given quantum state, and the RCC of the corresponding maximally entangled state. Moreover, for two-qubit systems we find a simple factorization law for the average remote-created coherence. [ABSTRACT FROM AUTHOR]

In this paper, we study entropic uncertainty relations on a finite-dimensional Hilbert space and provide several tighter bounds for multimeasurements, with some of them also valid for Rényi and Tsallis entropies besides the Shannon entropy. We employ majorization theory and actions of the symmetric group to obtain an admixture bound for entropic uncertainty relations for multimeasurements. Comparisons among all bounds for multimeasurements are given in two figures. [ABSTRACT FROM AUTHOR]

By combining a parameterized Hermitian matrix, the realignment matrix of the bipartite density matrix, and the vectorization of its reduced density matrices, we present a family of separability criteria which are stronger than the computable cross-norm or realignment (CCNR) criterion. With linear contraction methods, the proposed criteria can be used to detect the multipartite entangled states that are biseparable under any bipartite partitions. Moreover, we show by examples that the presented multipartite separability criteria can be more efficient than the corresponding multipartite realignment criterion based on CCNR, multipartite correlation tensor criterion, and multipartite covariance matrix criterion. [ABSTRACT FROM AUTHOR]

We study the local indistinguishability of mutually orthogonal product basis quantum states in the highdimensional quantum system. In the quantum system of Cd Cd, where d is odd, Zhang et al. [Z.-C. Zhang et al., Phys. Rev. A 90. 022313 (2014)] have constructed d² orthogonal product basis quantum states that are locally indistinguishable. We find a subset that contains 6d -- 9 orthogonal product states that are still locally indistinguishable. We generalize our method to an arbitrary bipartite quantum system €"' C". We present a small set with only 3(m + n) -- 9 orthogonal product states and prove that these states are local operations and classical communication (LOCC) indistinguishable. Even though these 3(m + n) -- 9 product states are LOCC indistinguishable, they can be distinguished by separable measurements. This shows that separable operations are strictly stronger than the local operations and classical communication. [ABSTRACT FROM AUTHOR]

We study the local unitary equivalence of arbitrary dimensional multipartite quantum mixed states. We present a necessary and sufficient criterion of the local unitary equivalence for general multipartite states based on matrix realignment. The criterion is shown to be operational, even for particularly degenerated states, by detailed examples. In addition, explicit expressions of the local unitary operators are constructed for locally equivalent states. Complementary to the criterion, an alternative approach based on the partial transposition of matrices is also given, which makes the criterion more effective in dealing with generally degenerated mixed states. [ABSTRACT FROM AUTHOR]

Based on relative entropy, we give a unified characterization of quantum correlations for nonlocality, steerability, discord, and entanglement for any bipartite quantum states. For two-qubit states we show that the quantities obtained from quantifying nonlocality, steerability, entanglement, and discord have strictly monotonic relationships. As examples, the Bell diagonal states are studied in detail. [ABSTRACT FROM AUTHOR]

The definition of accessible coherence is proposed. Through local measurement on the other subsystem and one-way classical communication, a subsystem can access more coherence than the coherence of its density matrix. Based on the local accessible coherence, the part that cannot be locally accessed is also studied, which we call it remaining coherence. We study how the bipartite coherence is distributed by partition for both l1 norm coherence and relative entropy coherence, and the expressions for local accessible coherence and remaining coherence are derived. We also study some examples to illustrate the distribution. [ABSTRACT FROM AUTHOR]