Bipartite entanglement in the spin-1/2 Ising-Heisenberg planar lattice constituted of identical trigonal bipyramidal plaquettes

The bipartite entanglement is rigorously examined in the spin-1/2 Ising-Heisenberg planar lattice composed of identical inter-connected bipyramidal plaquettes at zero and finite temperatures using the quantity called concurrence. It is shown that the Heisenberg spins of the same plaquette are twice stronger entangled in the two-fold degenerate quantum ground state than in the macroscopically degenerate quantum chiral one. The bipartite entanglement with chiral features completely disappears below or exactly at the critical temperature of the model, while that with no chirality may survive even above the critical temperature of the model. Non-monotonous temperature variations of the concurrence clearly evidence the activation of the entangled Heisenberg states also above classical ground state as well as their re-appearance above the critical temperature of the model.     

具有三角自旋环的伊辛-海森伯链的热纠缠

研究了具有三角自旋环的伊辛-海森伯链在磁场作用下的热纠缠性质.分别讨论了三角自旋环中自旋1/2粒子间相互作用的三种情形,即XXX,XXZ和XY Z海森伯模型.利用转移矩阵方法,数值计算了具有三角自旋环的伊辛-海森伯链的配对纠缠度.计算结果表明,外加磁场强度和温度对系统处于上述三种海森伯模型的热纠缠性质均有重要影响.给出了系统在不同的海森伯模型下,纠缠消失对应的临界温度随磁场强度的变化图,由此可以得到系统存在配对纠缠的参数区域,同时发现在特定的参数区域存在纠缠恢复现象.因此适当调节温度和磁场强度,可以有效调控具有三角自旋环的伊辛-海森伯链热纠缠性质.     

Concurrence and entanglement entropy in a dimerised spin-1/2 two-leg ladder

We consider isotropic spin-1/2 two-leg ladders with dominant spatially-modulated rung exchanges. We study the effect of a uniform magnetic field on the ground state phase diagram of the model using perturbation theory and the numerical Lanczos method. The ground state phase diagram consists of two gapless Luttinger liquid (LL) and three gapped phases. Numerically, we calculate the concurrence between two spins and the entanglement entropy between legs. Numerical experiment shows that the gapless LL phases are fundamentally different. In the first LL phase, only spins on rungs are entangled, but in the second LL phase the spins on legs are long-distance entangled. Therefore, the concurrence between spins on legs can be considered as a function to distinguish the LL phases.     

Multipartite Entanglement of a Tetrahedron Lattice

Three-dimensional Heisenberg model in the form of a tetrahedron lattice is investigated. The concurrence and multipartite entanglement are calculated through 2-concurrence C and 4-concurrence C4. The concurrence C and multipartite entanglement G4 depend on different coupling strengths Ji and are decreased when the temperature T is increased. For a symmetric tetrahedron lattice, the concurrence C is symmetric about J1 when J~ is negative while the multipartite entanglement G4 is symmetric about J1 when J2 〈 2. For a regular tetrahedron lattice, the concurrence G of ground state is 1/3 for ferromagnetic case while G = 0 for antiferromagnetic ca.se. However, there is no multipartitc entanglement since C4=0 in a regular tetrahedron lattice. The external magnetic field 13 can increase the maximum value of the concurrence GB and induce two or three peaks in Cn. There is a peak in the multipartite entanglement G4 B when G4B is varied as a function of the temperature T. This peak is mainly induced by the magnetic field B.     

Magnetic properties and concurrence for fluid 3He on kagome lattice

We present the results of magnetic properties and entanglement for kagome lattice using Heisenberg model with two- and three-site exchange interactions in strong magnetic field. Kagome lattice correspond to the third layer of fluid ³He absorbed on the surface of graphite. The magnetic properties and concurrence as a measure of pairwise thermal entanglement are studied by means of variational mean-field like treatment based on Gibbs-Bogoliubov inequality. The system exhibits different magnetic behaviors depending on the values of the exchange parameters (J ₂, J ₃). We have obtained the magnetization plateaus at low temperatures. The central theme of the paper is comparing the entanglement and magnetic behavior for kagome lattice. We have found that in the antiferromagnetic region behavior of the concurrence coincides with the magnetic susceptibility one.     

一维倾斜场伊辛模型中的纠缠特性

在一维倾斜场伊辛模型中, 利用并发度和Q测量函数分别对系统的两体纠缠和整体纠缠进行度量, 通过讨论系统中量子纠缠的动力学特性, 能够体现出系统的可积和不可积行为. 由系统基态的纠缠特性可以发现只要倾角不为零时, 系统的Q测量函数会随着磁场的增大而减少, 而用并发度刻画的系统的相变特性, 随着磁场倾角的增大发生了变化. 考虑系统的动力学行为发现, 在一维倾斜场伊辛模型中, 不可积性会抑制两体纠缠, 却促进系统整体纠缠生成. 关键词： 伊辛模型 不可积性 两体纠缠 整体纠缠     

Quantum entanglement in a two-electron quantum dot in magnetic field

The properties of quantum entanglement of the ground state in an exactly solvable model of a two-electron QD have been investigated. It is shown that the degree of entanglement increases with enhancement of interaction between electrons, irrespective of the shape of electron confining potential in a QD. A magnetic field destroys electron entanglement. However, the entanglement in deformed QDs is more stable against magnetic field.     

场与非线性介质原子相互作用模型的量子纠缠动力学特性

在场和非线性介质原子相互作用模型下, 利用concurrence和约化Neumann熵两种纠缠量度, 研究推广的二项式场态和原子基态的量子纠缠动力学. 结果表明concurrence与约化Neumann熵是正关联占优势; 在合适的条件下, 纠缠在较长时间内几乎是不变的. 这有利于量子信息过程. 关键词： 推广的二项式态 concurrence 约化Neumann熵     

Entanglement and Optimal Dense Coding in Spin Chain with an Arbitrary Magnetic Field

The entanglement and optimal dense coding at entangled states of a 1D Ising chain in the presence of an external magnetic field with an arbitrary direction, are investigated. The entanglement concurrence and the optimal dense coding capacity are calculated for different orientations of the magnetic field. It has been found that the direction of external magnetic field has effects on the entanglement concurrence and optimal dense coding capacity. In the case of antiferromagnet, the quantum phase transition occurs when an external magnetic field is parallel to Ising orientation. The concurrence increases when the angle between the direction of magnetic field and Ising orientation become smaller at ground state in certain parameter regimes, so does the optimal dense coding. The maximum moves toward the direction perpendicular to the Ising orientation in higher temperature. In contrast, the more concurrence and optimal dense coding can be produced only in the case of an external magnetic field perpendicular to Ising orientation at zero and low temperature for ferromagnetic case.     

Decoherence Effect in An Anisotropic Two-Qubit Heisenberg XYZ Model with Inhomogeneous Magnetic Field

Taking the decoherence effect into account, the entanglement evolution of a two-qubit anisotropic Heisenberg XYZ chain in the presence of inhomogeneous magnetic field is investigated. The time evolution of concurrence is studied for the initial state cos θ｜01） ＋ sin θ｜10） at zero temperature. The influences of inhomogeneous magnetic field, anisotropic parameter and decoherence on entanglement dynamic are addressed in detail, and a concurrence formula of the steady state is found. It is shown that the entanglement sudden death （ESD） and entanglement sudden birth （ESB） appear with the decoherence effect, and the stable concurrence depends on the uniform magnetic field B, anisotropic parameter △ and environment coupling strength γ, which is independent of different initial states and nonuniform magnetic field b.     

Entanglement in a two-qubit Heisenberg XXZ chain with different Dzyaloshinskii-Moriya couplings and an inhomogeneous magnetic field

Ground state entanglement and thermal entanglement of a two-qubit Heisenberg XXZ chain in the presence of the different Dzyaloshinski-Moriya interaction and inhomogeneous magnetic field are investigated.By the concept of concurrence, we find that the inhomogeneity of the magnetic field may make entanglement last for a long time and the critical temperature is dependent on Jz and b. The entanglement can be increased by increasing the temperature in some cases. We also find that the x-component parameter Dx has a higher critical temperature and more entanglement for a certain condition than the z-component parameter Dz.     

Entanglement of a Five-Qubit Heisenberg XX Chain in a Magnetic Field

We calculate the eigenvalues and eigenvectors of a five-qubit isotropic Heisenberg model in an external magnetic field, and give analytical results for the concurrence of two nearest-neighbor qubits. A magnetic field can eliminate degeneration and change the ground state of the system. Therefore increasing the value of the magnetic field can induce entanglement in a certain range both for the antiferromagnetic and ferromagnetic case.     

Thermal entanglement in a triple quantum dot system

We present studies of thermal entanglement of a three-spin system in triangular symmetry. Spin correlations are described within an effective Heisenberg Hamiltonian, derived from the Hubbard Hamiltonian, with super-exchange couplings modulated by an effective electric field. Additionally a homogenous magnetic field is applied to completely break the degeneracy of the system. We show that entanglement is generated in the subspace of doublet states with different pairwise spin correlations for the ground and excited states. For the doublets with the same spin orientation one can observe nonmonotonic temperature dependence of entanglement due to competition between entanglement encoded in the ground state and the excited state. The mixing of the states with an opposite spin orientation or with quadruplets (unentangled states) always monotonically destroys entanglement. Pairwise entanglement is quantified using concurrence for which analytical formulae are derived in various thermal mixing scenarios. The electric field plays a specific role – it breaks the symmetry of the system and changes spin correlations. Rotating the electric field can create maximally entangled qubit pairs together with a separate spin (monogamy) that survives in a relatively wide temperature range providing robust pairwise entanglement generation at elevated temperatures.     

Berry Phases and Entanglement of a Two Spin-1/2 Model with Dzyaloshinski-Moriya Interaction in Magnetic Fields

We show that the entanglement (as quantified by the concurrence) and Berry phases of the adiabatic quantum states vanish for a two spin-1/2 system with Dzyaloshinski-Moriya (DM) interaction, while one of the spins is driven by a time-varing rotating magnetic field and the other one is coupled with a strong static magnetic field. The system is described by the Heisenberg XX model and the static field is in the direction of the rotation axis. We also investigate that how the concurrence and Berry phases depend on the DM interaction, coupling coefficient and the static magnetic field. In addition, we show that reversing the sign of the static magnetic field can cause exchange of the Berry phases and entanglement between the adiabatic states. Finally it is shown that each energy level approach causes jumps or cusp-like behaviour in the Berry phases and the concurrences.     

Magnetic properties and quantum entanglement on decorated zigzag ladder

Magnetic properties and quantum entanglement of Heisenberg model with two-, three- and four-site exchange interactions on zigzag ladder are studied. Magnetic properties and concurrence (measure of quantum entanglement) are analyzed by means of variational mean-field-like treatment based on the Gibbs-Bogoliubov inequality. The magnetization plateau and second-order phase transition are obtained. A comparison of the entanglement and magnetic characteristics for the zigzag ladder is made. Our calculations show that in the antiferromagnetic region the behavior of the concurrence coincides with that of the magnetization.     

Effects of three-body interactions on the dynamics of entanglement in spin chains

With the consideration of three-body interaction, dynamics of pairwise entanglement in spin chains is studied. The dependence of pairwise entanglement dynamics on the type of coupling, and distance between the spins is analyzed in a finite chain for different initial states. It is found that, for an Ising chain, three-body interactions are not in favor of preparing entanglement between the nearest neighbor spins, while three-body interactions are favorable for creating entanglement between remote spins from a separable initial state. For an isotropic Heisenberg chain, the pairwise concurrence will decrease when three-body interactions are considered both for a separable initial state and for a maximally entangled initial state, however, three-body interactions will retard the decay of the concurrence in an Ising chain when the initial state takes the maximally entangled state.     

Quantum entanglement in exactly soluble atomic models: the Moshinsky model with three electrons,and with two electrons in a uniform magnetic field

We investigate the entanglement-related features of the eigenstates of two exactly soluble atomic models: a one-dimensional three-electron Moshinsky model, and a three-dimensional two-electron Moshinsky system in an external uniform magnetic field. We analytically compute the amount of entanglement exhibited by the wavefunctions corresponding to the ground, first and second excited states of the three-electron model. We found that the amount of entanglement of the system tends to increase with energy, and in the case of excited states we found a finite amount of entanglement in the limit of vanishing interaction. We also analyze the entanglement properties of the ground and first few excited states of the two-electron Moshinsky model in the presence of a magnetic field. The dependence of the eigenstates’ entanglement on the energy, as well as its behaviour in the regime of vanishing interaction, are similar to those observed in the three-electron system. On the other hand, the entanglement exhibits a monotonically decreasing behavior with the strength of the external magnetic field. For strong magnetic fields the entanglement approaches a finite asymptotic value that depends on the interaction strength. For both systems studied here we consider a perturbative approach in order to shed some light on the entanglement’s dependence on energy and also to clarify the finite entanglement exhibited by excited states in the limit of weak interactions. As far as we know, this is the first work that provides analytical and exact results for the entanglement properties of a three-electron model.     

Thermal Entanglement Properties in two Kinds of Two-qubit Spin Squeezing Model

Using the concurrence (C) criterion, we investigate the thermal entanglement properties in two-qubit spin squeezing model for two kinds of squeezing interaction: one-axis twisting model (OATM) and two-axis countertwisting model (TACM) with a transverse field. To the OATM, in the limit case of T→0, the ground state entanglement is initially increased from zero to the maximum value, then decreased in a period of time and suddenly disappeared finally with further enhancing the external magnetic field Ω. One interesting thing is that instead of decaying slowly to zero the entanglement is sudden disappeared with further enhancing Ω or μ (the spin squeezing interaction in X direction), and decreasing the parameter μ or Ω can obviously broaden the scope of entanglement exists. For the finite temperature case, a novelty point is the sudden birth phenomenon occured in the behaviors of entanglement, it is initially to be zero (persists for some time), with further improving Ω and μ the entanglement will be suddenly appeared, and the time interval (persists to be zero) before sudden birth is obviously prolonged with decreasing two parameters. The temperature range of entanglement exists can be extended evidently with increasing μ or Ω, and one can obtain entanglement at higher temperature through changing them. When to the TACM, the ground state entanglement is initially decreased from the maximum value and then suddenly disappeared with increasing Ω. While increasing γ the ground state entanglement is increased initially from zero to the maximum value and then sudden disappeared with further improving γ (the spin squeezing interaction in XY plane), proper tuing γ or Ω can prolong the lives of entanglement evidently. For the finite temperature case, the sudden birth phenomenon also occured in the the evoluted concurrence, the variation of parameters Ω and γ can reduce the time interval before sudden birth. The influence of the temperature T on thermal entanglement property is also investigated. The temperature range of entanglement existence can be extended evidently with increasing γ, one can obtain entanglement at higher temperature through changing parameters γ and Ω.     

Dynamics of entanglement in two-qubit open system interacting with a squeezed thermal bath via dissipative interaction

We study the dynamics of entanglement in a two-qubit system interacting with a squeezed thermal bath via a dissipative system-reservoir interaction with the system and reservoir assumed to be in a separable initial state. The resulting entanglement is studied by making use of concurrence as well as a recently introduced measure of mixed state entanglement via a probability density function which gives a statistical and geometrical characterization of entanglement by exploring the entanglement content in the various subspaces spanning the two-qubit Hilbert space. We also make an application of the two-qubit dissipative dynamics to a simplified model of quantum repeaters.     

Quantum Teleportation via a Two-Qubit Ising Heisenberg Chain with an Arbitrary Magnetic Field

The quantum teleportation via a two-qubit Ising Heisenberg chain in the presence of an external magnetic field with an arbitrary direction are investigated. The effect of the orientation of an external magnetic field on the entanglement teleportation has been analyzed numerically. It is found that the teleported thermal concurrence and average fidelity can be maximized by rotating the magnetic field (with fixed magnitude) to an optimal direction. The ferromagnetic channel is not suitable to teleportation. A minimal entanglement of the thermal state is needed to realize the entanglement teleportation for antiferromagnetic channel. It is also found that the entanglement of the channel cannot completely reflect the teleported concurrence and average fidelity. There exist double-value phenomena between them.