General Properties of Thermal Entanglement in an Arbitrary-Length Heisenberg Spin Chain

We investigate general properties of thermal entanglement in arbitrary-length 1D Helsenberg spin-1/2 chain based on classifications of its eigenstates. The influences of magnetic field and temperature on entanglement are qualitatively discussed and three features are presented. The conclusions hold for both bipartite and multipartite entanglement, and are in agreement with the results numerically proven by Arnesen et al. [Phys. Rev. Lett. 50 （2001） 017901].     

Entanglement in One-Dimensional Random XY Spin Chain with Dzyaloshinskii--Moriya Interaction

The impurities of exchange couplings, external magnetic fields and Dzyaloshinskii-Moriya （DM） interaction considered as Gaussian distribution, and the entanglement in one-dimensional random XY spin systems is investigated by the method of solving the different spin-spin correlation functions and the average magnetization per spin. The entanglement dynamics at central locations of ferromagnetic and antiferromagnetic chains have been studied by varying the three impurities and the strength of DM interaction. （i） For the ferromagnetic spin chain, the weak DM interaction can improve the amount of entanglement to a large value, and the impurities have the opposite effect on the entanglement below and above critical DM interaction. （ii） For the antiferromagnetic spin chain, DM interaction can enhance the entanglement to a steady value. Our results imply that DM interaction strength, the impurity and exchange couplings （or magnetic field） play competing roles in enhancing quantum entanglement.     

Effects of Inhomogeneous Spin Coupling and Anisotropy on Thermal Entanglement

We study the thermal entanglement properties of a simple system that includes three spins inhomogeneously coupled between them with additional anisotropy in their couplings. The main result is the systematic analysis of the concurrence evolution as functions of inhomogeneity, anisotropy and temperature. By adjusting proportional factor of the interaction J and anisotropy parameter △, the comparison between concurrences C₁₂ andC₁₃ is also presented.     

Boundary Quantum Entanglement of the XXZ Spin Chain with Boundary Impurities

The boundary quantum entanglement for the s = 1/2 X X Z spin chain with boundary impurities is studied via the density matrix renormalization group （DMRG） method. It is shown that the entanglement entropy of the boundary bond （the impurity and the chain spin next to it） behaves differently in different phases. The relationship between the singular points of the boundary entropy and boundary quantum critical points is discussed.     

Sudden Death, Birth and Stable Entanglement in a Two-Qubit Heisenberg XY Spin Chain

Taking the decoherence effect due to population relaxation into account, we investigate the entanglement properties for two qubits in the Heisenberg XY interaction and subject to an external magnetic field. It is found that the phenomenon of entanglement sudden death (ESD) as well as sudden birth (ESB) appear during the evolution process for particular initial states. The influence of the external magnetic field and the spin environment on ESD and ESB are addressed in detail. It is shown that the concurrence, a measure of entanglement, can be controlled by tuning the parameters of the spin chain, such as the anisotropic parameter, external magnetic field, and the coupling strength with their environment. In particular, we find that a critical anisotropy constant exists, above which ESB vanishes while ESD appears. It is also notable that stable entanglement, which is independent of different initial states of the qubits, occurs even in the presence of decoherence.     

Thermal Entanglement of Anisotropic XY Chains in a Transverse Field

By using the concept of concurrence, we numerically investigate the thermal entanglement between any two nearest-neighbour spins in uniform and periodic anisotropic XY chains in a transverse field at finite temperature T. It is found that the entanglement has more than one critical temperatures on some parameter regions for uniform and periodic chains. We also discuss the behaviour of the thermal entanglement at the vicinity of quantum phase transition of periodic anisotropic XY chains and find that a11 the derivatives aλC have similar behaviour as that of the uniform chain.     

Entanglement in a quantum mixed-spin chain

The pairwise entanglement between neighboring spins in a general mixed-spin chain with arbitrary spins S and 1/2 is investigated in the thermodynamical limit. The entanglement is witnessed by the magnetic susceptibility which determines a characteristic temperature for an entangled thermal state. The characteristic temperature is nearly proportional to the interaction J and the mixed-spin S. The bound of negativity is obtained on the basis of the magnetic susceptibility. It is found that the macroscopic magnetic properties are affected by the quantum entanglement in the real solids.     

Thermal Entanglement in the Anisotropic Heisenberg XYZ Model with Different Dzyaloshinskii-Moriya Couplings

Thermal entanglement is investigated in a two-qubit Heisenberg XYZ system with different Dzyaloshinskii Moriya （DM） couplings. It is shown that different DM interaction parameters have different influences on the entanglement and the critical temperature. In addition, according to the relation between the real coupling coefficients Jx and Jz, a more efficient DM control parameter can be obtained by adjusting the direction of DM interaction.     

Generation of Long-Distance Entanglement in Spin System

We propose two schemes to produce long-distance entanglement in a spin chain. The first is based on a controllable interaction system, one starts from an entangled kernel and adds weaken interaction spins to the boundary sites step by step, then the entanglement will be extended longer and longer and its value is equal to that of its kernel. The second is based on a uniform interaction （J） system with a bulk magnetic field （B） that is absent for the boundary qubits, as long as B/J 〉 5, one can obtain near perfect long distance entanglement. Ultra-low temperature is needed in both schemes.     

Entanglement dynamics of a three-qubit system interacting with a quantum spin environment

We investigate the entanglement dynamics and decoherence of a three-qubit system under a quantum spin environment at a finite temperature in the thermodynamics limit. For the case under study, we find the evolution of pairwise entanglement depends not only on the initial states but also on the parameters related to the system and the spin environment. In addition, an undesirable entanglement sudden death occurs in the process of entanglement evolution, and this effect can be controlled by the coupling constant between two qubits, external magnetic field, and the interaction between the system and the environment.     

Dynamics of Genuine Three-Qubit Entanglement in Ising Spin Systems

We investigate the dynamics of genuine three-qubit entanglement in the Ising model of three spins. A scheme is presented for generating the genuine three-qubit entanglement by the nearest-neighbour couplings. The effect of magnetic fields on the dynamics of genuine three-qubit entanglement is also discussed.     

Entanglement in the Ground State of an Isotropic Three-Qubit Transverse XY Chain with Energy Current

The ground state entanglement in an isotropic three-qubit transverse XY chain with energy current is analysed. A quantum phase transition from a no-energy-current phase to energy-current phase is found when the magnetic field changes. It has also been found that the ground state changes in company with the quantum phase transition.     

Entanglement in a spin-one spin chain

The thermal entanglement in a two-spin-qutrit system with two spins coupled by exchange interaction is investigated in terms of the measure of entanglement called ‘negativity’. We strictly show that for any temperature the entanglement is symmetric with respect to zero magnetic field. The behavior of negativity is presented for four different cases. We find that the entanglement may be enhanced under a nonuniform magnetic field. Because there is not any necessary and sufficient condition for quantum separability in systems of dimension 3⊗3, our results are qualitative, not quantitative.     

Thermal entanglement of a two-qutrit Ising system with Dzialoshinski-Moriya interaction

Thermal entanglement of a two-qutrit Ising system in the presence of an external homogeneous magnetic field and Dzialoshinski-Moriya (DM) interaction is investigated. Influences of magnetic field, temperature, and DM interaction on the entanglement have been characterized in terms of negativity for a wide range of parameters. The cases of parallel, antiparallel and transverse magnetic fields are considered. Results of detailed numerical calculations are explained using the analytically determined ground and excited states of the system. It is shown that at a given temperature, control of entanglement can be optimized by utilizing competing effects of the magnetic field and the DM interaction.     

Entanglement in Anisotropic Heisenberg XYZ Chain with Inhomogeneous Magnetic Field

The thermal entanglement of a two-qubit anisotropic Heisenberg XYZ chain under an inhomogeneous magnetic field b is studied. It is shown that when inhomogeneity is increased to a certain value, the entanglement can exhibit a larger revival than that of less values of b. The property is both true for zero temperature and a finite temperature. The results also show that the entanglement and threshold temperature can be increased by increasing inhomogeneous external magnetic field.     

Entanglement in Anisotropic Heisenberg XYZ Chain with Inhomogeneous Magnetic Field

The thermal entanglement of a two-qubit anisotropic Heisenberg XYZ chain under an inhomogeneous magnetic field b is studied. It is shown that when inhomogeneity is increased to a certain value, the entanglement can exhibit a larger revival than that of less values of b. The property is both true for zero temperature and a finite temperature. The results also show that the entanglement and threshold temperature can be increased by increasing inhomogeneous external magnetic field.     

Remote State Preparation with Genuine Multipartite Entanglement

Enlightened by the work of Yeo and Chua [Phys. Rev. Lett. 96 （2006） 060502] for teleportation and dense coding with genuine multipartite entanglement, we present an explicit protocol for faithful remote state preparation in a real coefficient case by using the same four-particle entangled state which is not reducible to pair of Bell states. It is shown that any complex coefficient case can be changed to a real coefficient case. With this protocol, the state can play an analogous role to Einstein-Podolsky-Rosen pairs in the theory of multipartite entanglement.     

Linear Entropy and Entanglement in Two-Charge-Qubit Circuits

We consider a model that contains two coupled superconducting charge qubits by sharing a large Josephson junction. We examine the dynamical properties of the linear entropy of two qubits and the probability of both qubits being in an excited state. The results show that the initial mean photon number, the initial phase of the field and the relative phase of the two qubits＇ levels play an important role in the evolution of the linear entropy of the two qubits and the probability.     

Entanglement in eight-qubit graph states

Any 8-qubit graph state belongs to one of the 101 equivalence classes under local unitary operations within the Clifford group. For each of these classes we obtain a representative which requires the minimum number of controlled-Z gates for its preparation, and calculate the Schmidt measure for the 8-partite split, and the Schmidt ranks for all bipartite splits. This results into an extension to 8 qubits of the classification of graph states proposed by Hein, Eisert, and Briegel [M. Hein, J. Eisert, H.J. Briegel, Phys. Rev. A 69 (2004) 062311].     

Entanglement of Bell diagonal mixed states

A sufficient and necessary condition for separability of Bell diagonal mixed states for bipartite systems in higher dimensions is presented. Moreover, we present a necessary condition for genuine entanglement of Bell diagonal mixed states in higher dimensions for multipartite systems.