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.     

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.     

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.     

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.     

Effects of Dzyaloshinski-Moriya anisoyropic antisymmetric interaction on entanglement and teleportation in a two-qubit Heisenberg chain with intrinsic decoherence

We studied the effects of Dzyaloshinski-Moriya (DM) anisoyropic antisymmetric interaction on entanglement and teleportation in a two-qubit Heisenberg chain with intrinsic decoherence taken into account. The main result is the systematic analysis of the negativity and fully entangled fraction’s evolution as a function of DM interaction D and time t. The contrast between the case of the maximally entangled initial state and unentangled ones is presented.     

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.     

Spin bath decoherence of quantum entanglement

We study an analytically solvable model for decoherence of a two spin system embedded in a large spin environment. As a measure of entanglement, we evaluate the concurrence for the Bell states (Einstein-Podolsky-Rosen pairs). We find that while for two separate spin baths all four Bell states lose their coherence with the same time dependence, for a common spin bath, two of the states decay faster than the others. We explain this difference by the relative orientation of the individual spins in the pair. We also examine how the Bell inequality is violated in the coherent regime. Both for one bath and two bath cases, we find that while two of the Bell states always obey the inequality, the other two violate the inequality at early times.     

Pairwise entanglement of a three-qubit Heisenberg XY chain in a nonuniform magnetic field with intrinsic decoherence

Taking into account the intrinsic decoherence, the concurrence of the nearest and the next-to-nearest neighbor qubits in a three-qubit Heisenberg XY chain are investigated when a nonuniform magnetic field is included. We show that the effects of the external magnetic field, including the uniform and inhomogeneous magnetic fields, on the time evolution of entanglement between the nearest and the next-to-nearest neighbor qubits rely deeply on the initial states. We can moderate the destructive effect of intrinsic decoherence by controlling the uniform and inhomogeneous magnetic fields, so that a proper value of uniform and inhomogeneous magnetic fields can, to a great extent enhance the stationary entanglement.     

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.     

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.     

Threshold temperature of thermal entanglement in an XXZ ferromagnetic chain

Pairwise thermal entanglement of an XXZ ferromagnetic chain with a uniform magnetic field is investigated by using the entanglement measure of negativity. The effects of spin, number of sites, anisotropic parameter, and magnetic field on the threshold temperature are discussed respectively.     

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.     

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 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.     

Thermal entanglement of a two-qutrit XX spin chain with Dzialoshinski-Moriya interaction

The effect of Dzialoshinski-Moriya (DM) interaction on thermal entanglement of a two-qutrit XX spin chain in a homogenous magnetic field is investigated. Our results imply that DM interaction and the magnetic field play competing roles in enhancing thermal entanglement.     

Interplay between the Dzyaloshinskii–Moriya anisotropic antisymmetric interaction and the SWAP operation in a two-qubit Heisenberg model

The SWAP operation in a two-qubit Heisenberg model in the presence of Dzyaloshinskii–Moriya (DM) anisotropic antisymmetric interaction is investigated. It is shown that the SWAP operation can be implemented for some kinds of DM coupling and the influence of DM couplings is divided into different cases. The conditions of the DM coupling under which the SWAP operation is feasible are established.     

Entangling power of a two-qudit geometric phase gate

We construct a geometric quantum phase shift gate for qudits in NMR systems. We study the operator entanglement and entangling power of the geometric gate for quantum computations.     

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.     

Thermal entanglement in the anisotropic Heisenberg XYZ model with different inhomogeneous magnetic fields

Thermal entanglement is investigated in a two-qubit Heisenberg XYZ system with different inhomogeneous magnetic fields. It is found that different magnetic fields have different entanglement and critical values. In addition, according to the relation of spin-spin coupling coefficients, a more efficient control parameter of magnetic field can be obtained by adjusting the direction of external magnetic field.     

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.