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We study the entanglement of a multipartite quantum state. An inequality between the bipartite concurrence and the multipartite concurrence is obtained. More effective lower and upper bounds of the multipartite concurrence are obtained. By using the lower bound, the entanglement of more multipartite states is detected. [ABSTRACT FROM AUTHOR]

• The system consists of two acoustic wave resonator, two ensembles of nitrogen-vacancy centers, and a superconducting resonator. • The interaction is nonlocal. • Generate the Bell state and construct the controlled-phase gate. We study the generation of entanglement and the realization of controlled quantum phase gates in hybrid quantum systems. Based on the researches on acoustic wave resonators (AWRs) in recent years, we propose a hybrid system which consists of two high quality-factor AWRs, two ensembles of nitrogen-vacancy-centers (NVEs), and a superconducting resonator used to interact two NVEs. Utilizing this hybrid system we present detailed schemes to produce entangled states and carry out controlled-phase gates on two distant AWRs. The numerical simulation shows that from our protocols the fidelities of the entangled states and the controlled-phase gates can reach 99.19 % and 98.56 %, respectively, by taking into account the dissipation and dephasing of the whole system. [ABSTRACT FROM AUTHOR]

Abstract: We construct a set of PPT (positive partial transpose) states and show that these PPT states are not separable, thus present a class of bound entangled quantum states. [Copyright &y& Elsevier]

Approximation of matrices to the sum of tensor products of Hermitian matrices is studied. A minimum decomposition of matrices on tensor space H 1 ⨂ H 2 in terms of the sum of tensor products of Hermitian matrices on H 1 and H 2 is presented. From this construction the separability of quantum states is discussed. [Copyright &y& Elsevier]

Abstract: In terms of the analysis of fixed point subgroup and tensor decomposability of certain matrices, we study the equivalence of quantum bipartite mixed states under local unitary transformations. For non-degenerate case an operational criterion for the equivalence of two such mixed bipartite states under local unitary transformations is presented. [Copyright &y& Elsevier]

Abstract: We investigate the equivalence of quantum states under local unitary transformations. A complete set of invariants under local unitary transformations is presented for a class of mixed states. It is shown that two states in this class are locally equivalent if and only if all these invariants have equal values for them. [Copyright &y& Elsevier]

Abstract: The multipartite entangled state for the total momentum and relative coordinates of n particles is constructed. The corresponding quantum-mechanical operator with respect to the classical transformation , , , in the state is investigated. [Copyright &y& Elsevier]

We present a kind of construction for a class of special matrices with at most two different eigenvalues, in terms of some interesting multiplicators which are very useful in calculating eigenvalue polynomials of these matrices. This class of matrices defines a special kind of quantum states — d-computable states. The entanglement of formation for a large class of quantum mixed states is explicitly presented. [Copyright &y& Elsevier]

Explicit sufficient and necessary conditions for separability of N-dimensional rank two multiparty quantum mixed states are presented. A nonseparability inequality is also given, for the case where one of the eigenvectors corresponding to nonzero eigenvalues of the density matrix is maximally entangled. [Copyright &y& Elsevier]

We study mutually unbiased bases (MUBs) in which all the bases are unextendible maximally entangled ones. We first present a necessary and sufficient condition of constructing a pair of MUBs in C 2 ⊗ C 4. Based on this condition, an analytical and necessary condition for constructing MUBs is given. Moreover we illustrate our approach by some detailed examples in C 2 ⊗ C 4. The results are generalized to C 2 ⊗ C d (d ≥ 3) and a concrete example in C 2 ⊗ C 8 is given. [ABSTRACT FROM AUTHOR]

We calculate analytically the one-way deficit for systems consisting of spin- j and spin- 1 2 subsystems with SU(2) symmetry. Comparing our results with the quantum discord of SU(2) invariant states, we show that the one-way deficit is equal to the quantum discord for half-integer j , and is larger than the quantum discord for integer j . Moreover, we also compare the one-way deficit with entanglement of formation. The quantum entanglement tends to zero if j increases, while the one-way deficit can remain significantly large. [ABSTRACT FROM AUTHOR]

We study the optimal entanglement witness with respect to multiqubits W-states. We show such entanglement witnesses can be used to distinguish genuine entangled states, different biseparable states and fully separable states. [Copyright &y& Elsevier]

We give explicit expressions for entanglement measures of Werner states in arbitrary dimensions in terms of concurrence and tangle. We show that an optimal ensemble decomposition for a joint density matrix of a Werner slate can achieve the minimum average concurrence and tangle simultaneously. Furthermore, the same decomposition also altains entanglement of formation for Werner slates. [Copyright &y& Elsevier]

In previous work the authors introduced the notion of generic states and obtained criteria for local equivalence of them. Here they introduce the concept of CHG states maintaining the criteria of local equivalence. This fact allows the authors to halve the number of invariants necessary to characterize the equivalence classes under local unitary transformations for the set of tripartite states whose partial trace with respect to one of the subsystems belongs to the class of CHG mixed states. [Copyright &y& Elsevier]

The equivalence problem under local unitary transformation for n-partite pure states is reduced to the one for (n-1)-partite mixed states. In particular, a tripartite system ℋ A ⊗ ℋ B ⊗ ℋ C ⊗, where ℋ j ; is a finite-dimensional complex Hilbert space for j=A, B, C, is considered and a set of invariants under local transformations is introduced, which is complete for the set of states whose partial trace with respect to ℋ A belongs to the class of generic mixed states. [Copyright &y& Elsevier]

We investigate the differential geometry of bipartite quantum states. In particular, the manifold structures of pure bipartite states are studied in detail. The manifolds with respect to all normalized pure states of arbitrarily given Schmidt ranks or Schmidt coefficients are explicitly presented. The dimensions of the related manifolds are calculated. [Copyright &y& Elsevier]