Abstract:
The pair coherent state is a state of a two-mode radiation field which is known as a state with non-Gaussian wave function. In this paper, the upper and lower bounds for D-concurrence (a new entanglement measure) have been studied over this state and calculated.

Abstract:
We present an unifying approach to the quantification of entanglement based on entanglement witnesses, which includes several already established entanglement measures such as the negativity, the concurrence and the robustness of entanglement. We then introduce an infinite family of new entanglement quantifiers, having as its limits the best separable approximation measure and the generalized robustness. Gaussian states, states with symmetry, states constrained to super-selection rules and states composed of indistinguishable particles are studied under the view of the witnessed entanglement. We derive new bounds to the fidelity of teleportation d_{min}, for the distillable entanglement E_{D} and for the entanglement of formation. A particular measure, the PPT-generalized robustness, stands out due to its easy calculability and provides sharper bounds to d_{min} and E_{D} than the negativity in most of states. We illustrate our approach studying thermodynamical properties of entanglement in the Heisenberg XXX and dimerized models.

Abstract:
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 state can achieve the minimum average concurrence and tangle simultaneously. Furthermore, the same decomposition also attains entanglement of formation for Werner states.

Abstract:
We obtain a simplified and obvious expression of "concurrence" in Wootters' measure of entanglement of a pair of qubits having no more than two non-zero eigenvalues in terms of concurrences of eigenstates and their simple combinations. It not only simplifies the calculation of Wootters' measure of entanglement, but also reveals some its general and important features. Our conclusions are helpful to understand and use quantum entanglement further.

Abstract:
Maximal correlation is a measure of correlation for bipartite distributions. This measure has two intriguing features: (1) it is monotone under local stochastic maps; (2) it gives the same number when computed on i.i.d. copies of a pair of random variables. This measure of correlation has recently been generalized for bipartite quantum states, for which the same properties have been proved. In this paper, based on maximal correlation, we define a new measure of entanglement which we call maximal entanglement. We show that this measure of entanglement is faithful (is zero on separable states and positive on entangled states), is monotone under local quantum operations, and gives the same number when computed on tensor powers of a bipartite state.

Abstract:
We explicitly show a protocol in which an arbitrary two qubit a|00> + b|01> + c|10> + d|11> is faithfully and deterministically teleported from Alice to Bob. We construct the 16 orthogonal generalized Bell states which can be used to teleport the two qubits. The local operations Bob must perform on his qubits in order to recover the teleported state is also constructed. They are restricted only to single qubit gates. This means that a CNOT gate is not necessary to complete the protocol. A generalization where N qubits is teleported is also shown. We define a generalized magic basis, which possesses interesting properties. These properties help us to suggest a generalized concurrence from which we construct a new measure of entanglement that has a clear physical interpretation: A multipartite state has maximum entanglement if it is a genuine quantum teleportation channel.

Abstract:
We define the concurrence hierarchy as d-1 independent invariants under local unitary transformations in d-level quantum system. The first one is the original concurrence defined by Wootters et al in 2-level quantum system and generalized to d-level pure quantum states case. We propose to use this concurrence hierarchy as measurement of entanglement. This measurement does not increase under local quantum operations and classical communication.

Abstract:
Hilbert-Schmidt distance reduces to Euclidean distance in Bell decomposable states. Based on this, entanglement of these states are obtained according to the protocol proposed in Ref. [V. Vedral et al, Phys. Rev. Lett. 78, 2275 (1995)] with Hilbert-Schmidt distance. It is shown that this measure is equal to the concurrence and thus can be used to generate entanglement of formation. We also introduce a new measure of distance and show that under the action of restricted LQCC operations, the associated measure of entanglement transforms in the same way as the concurrence transforms .

Abstract:
In this paper, we investigate spin entanglement in the $XXZ$ model defined on a $d$-dimensional bipartite lattice. The concurrence, a measure of the entanglement between two spins, is analyzed. We prove rigorously that the ground state concurrence reaches maximum at the isotropic point. For dimensionality $d \ge 2$, the concurrence develops a cusp at the isotropic point and we attribute it to the existence of magnetic long-range order.

Abstract:
Via a multidimensional complementarity relation we derive a novel operational entanglement measure for any discrete quantum system, i.e. for any multidimensional and multipartite system. This new measure admits a separation into different classes of entanglement obtained by using a flip operator 2,3,...,n times, defining a m-flip concurrence. For mixed states bounds on this m-flip concurrence can be obtained. Moreover, the information content of a n partite multidimensional system admits an intuitive interpretation. Explicitly, the three qubits system is analyzed and the physical difference in entanglement of the W-state, the GHZ state or the bi-separable state is revealed.