Narrow Results

Pairwise entanglement properties of a symmetric multi-qubit system are analyzed through a complete set of two-qubit local invariants. Collective features of entanglement, such as spin squeezing, are expressed in terms of invariants and a classification scheme for pairwise entanglement is proposed. The invariant criteria given here are shown to be related to the recently proposed (Phys. Rev. Lett.95, 120502 (2005)) generalized spin squeezing inequalities for pairwise entanglement in symmetric multi-qubit states.

We study ground-state pairwise entanglement of spins in mean field clusters of spin-one particles interacting via the Ising interaction in the presence of longitudinal and transverse crystal fields. A general result is found that for all kinds of the spin-one Ising models, the pairwise negativities are symmetric with respect to the zero values of the applied transverse or longitudinal magnetic fields. For models considered in this paper, we show numerically that the crystal fields can serve as an alternative tool to create "on-demand" ground-state entanglement for small clusters of spins.

The zero-temperature pairwise entanglement is investigated in the antiferromagnetic Heisenberg chain with one impure spin s. The impurity location is varied from the open end to a mediate site of the spin chain. It is found that the pairwise entanglement is proportional to 1/s. This means that the entanglement will disappear in the classical systems as s → ∞. Compared to the isotropic Heisenberg chain without impurity, the efficient control of the spin coupling between the impurity spin and nearest-neighbor spins can enhance the pairwise entanglement.

By using the concept of concurrence, we study pairwise entanglement between the two end spins in the open-ended Heisenberg XXX and XY chains up to ten spins. The results show that by introducing two boundary impurities, one can obtain maximum entanglement at the limit of the impurity parameter |J₁| ≪ J for the even-number qubits. When |J₁/J| > 0, the entanglement always decreases with the increase in the absolute value of J₁/J, and for the Heisenberg XXX chain, C disappears when J₁/J exceeds a certain critical point J_ic, and attains an asymptotic value C₀ when |J₁| ≫ J(J₁ < 0), while for the Heisenberg XY chain, C always disappears when |J₁/J| exceeds a certain critical point J_ic. Both C₀ and J_ic decrease with the increase of the length of the chain.

The pairwise entanglement dynamics in a multipartite system consisting of three two-level atoms A, B, C and a single-mode cavity field a is studied via negativity. Three atoms are arranged in such a way that atoms BC are embedded in and locally interact with the cavity while atom A is located in a spatially separate place outside of the cavity. Initially, atom-pair AB is prepared in a Bell-like state while atom C in a superposition of ground and excited state, |g_C〉 and |e_C〉. It shall be shown that all the pairwise negativities of the total system including atoms and cavity undergo qualitatively different evolutions. The so-called entanglement sudden death is observed for atom-pair AB under certain conditions and the entanglement transfer among all the possible degrees of freedom of the whole system is also discussed.

We investigate the effects of anisotropy on the dynamic evolution of pairwise entanglement in the four-qubit Heisenberg XXZ model. The entanglement between the nearest-neighbor and the next nearest-neighbor qubits are calculated by making use of concurrence. Our results show that the sudden death effect can be weakened when introducing the anisotropy Δ. In addition, we also find that the anisotropy Δ can protect the entanglement between the nearest-neighbor qubits from being completely destroyed by the intrinsic decoherence, but it cannot do this for the entanglement between the next nearest-neighbor qubits.

For a three-qubit Heisenberg XX spin chain with the uniform magnetic field and magnetic impurity, dynamic evolution of pairwise entanglement are studied. We show that the phenomenon of entanglement sudden death (ESD) occurs in the evolution of entanglement for some initial states. We also find that magnetic impurity cannot only eliminate the phenomenon of ESD but also induce the ESD effects, which is different from the case of uniform magnetic field where the ESD can be depressed but cannot be eliminated by introducing the uniform magnetic field.