Effects of inhomogeneous magnetic fields and different Dzyaloshinskii- Moriya interaction on entanglement and teleportation in a two-qubit Heisenberg XYZ chain

In this paper we calculate the thermal entanglement and teleportation in a two-qubit Heisenberg XYZ chain with the different Dzyaloshinskii-Moriya interaction and inhomogeneous magnetic fields. The analytical expres- sions of the concurrence and the average fidelity are obtained for this model. We have shown that the quantum phase transition occurs in the system and the quantum phase transition point depends on the inhomogeneity of magnetic fields. We compare the x-component Dzyaloshinskii-Moriya interaction with the z-component Dzyaloshinskii-Moriya interaction on the effects of quantum teleportation. It is found that we can take Dzyaloshinskii-Moriya interaction as one of the effective control parameters for the teleportation manipulation.     

Thermal entanglement and teleportation in a two-qubit Heisenberg XXZ chain with different Dzyaloshinskii-Moriya interactions

We study the thermal output entanglement and teleportation in a two qubit Heisenberg XXZ chain with different Dzyaloshinskii-Moriya (DM) interactions. The analytical expressions of the output entanglement and the average fidelity are obtained for this model. We find the entanglement of replica states will be induced by some large value of D_z and the output entanglement exists for the case of J_z < − 1. The influences of the different DM interactions on the fidelity of teleportation are studied. We show that by introducing the x-component DM interaction, the average fidelity F_A can reach its maximum value 1.     

Effects of Dzyaloshinskii-Moriya interaction on thermal entanglement and teleportation via a two-qubit Heisenberg XXZ spin chain under external magnetic field

This paper mainly investigates the effects of different Dzyaloshinskii-Moriya (DM) anisotropic antisymmetric interactions on thermal entanglement and teleportation of one-qubit state in both the standard and non-standard protocols as well as the partial teleportation of an entangled state via a two-qubit Heisenberg XXZ spin chain in the presence of external magnetic fields. The dependency of the thermal entanglement and average fidelity on various system parameters is analyzed. The interplay of the different parameters on the teleportation is discussed. The DM interaction is found to be effective for the thermal entanglement in the spin chain both with and without external magnetic fields. However, it turned out to be destructive for the teleportation in the standard protocol, whereas is found constructive for single qubit teleportation when the spin chain with the z-direction parameters is used as the channel in the non-standard protocol. Moreover, the results show that, for teleporting one-qubit state, the antiferromagnetic (AFM) chain is the only qualified candidate in the standard protocol, while both the AFM and ferromagnetic (FM) chains with the parameters along the z-axis are all suitable in the non-standard protocol when the parameters are chosen appropriately. For the partial teleportation of entanglement, both the AFM and FM chains are eligible as long as the appropriate combinations of parameters are chosen. In addition, the comparison of the effects of the same, fixed x- and z-component parameters of the DM interaction (D_x and D_z) on teleportation is presented.     

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 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.     

非匀强磁场中双量子位Heisenberg XY链的基态纠缠和热纠缠(英文)

研究了非匀强磁场中各向异性Heisenberg XY链的基态纠缠和热纠缠.结果表明对双量子位情形,纠缠与格点间耦合常数J、外部磁场B、各向异性参数γ和b的正负无关.对绝对零度情形,我们给出了纠缠C的解析表达式,并指出临界磁场Bc随磁场各向异性参数b的增大而增大.对有限温度情形,我们给出了γ=0时C的解析表达式和γ≠0时的数值模拟结果,结果发现引进非匀强磁场可以使纠缠在某些区域明显增大;同时我们还指出当γ=0时,纠缠存在的临界温度Tc仅是b的增函数,而当γ≠0时,它却由B和b共同决定.     

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.     

Bipartite entanglement in a two-qubit Heisenberg XXZ chain under an inhomogeneous magnetic field

This paper investigates the bipartite entanglement of a two-qubit Heisenberg XXZ chain under an inhomogeneous magnetic field. By the concept of negativity, we find that the inhomogeneity of the magnetic field may induce entanglement and the critical magnetic field is independent of Jz. We also find that the entanglement is symmetric with respect to a zero magnetic field. The anisotropy parameter Jz may enhance the entanglement.     

Bipartite entanglement in a two-qubit Heisenberg XXZ chain under an inhomogeneous magnetic field

This paper investigates the bipartite entanglement of a two-qubit Heisenberg XXZ chain under an inhomogeneous magnetic field. By the concept of negativity, we find that the inhomogeneity of the magnetic field may induce entanglement and the critical magnetic field is independent of Jz. We also find that the entanglement is symmetric with respect to a zero magnetic field. The anisotropy parameter Jz may enhance the entanglement.     

Non-equilibrium entanglement dynamics of a two-qubit Heisenberg XY system in the presence of an inhomogeneous magnetic field and spin-orbit interaction

Entanglement dynamics of an open two-qubit anisotropic XY Heisenberg system is investigated in the presence of an inhomogeneous magnetic field and spin-orbit interaction. We suppose that each qubit interacts with a separate thermal reservoir which is held in its own temperature. The asymptotical and the dynamical behavior of entanglement are analyzed. To distinguish between entanglement induced by the environment and entanglement due to the presence of inter-qubit interaction, the effects of spin-orbit parameter D and temperature difference parameter ΔT on the entanglement of the system have been investigated. We show that for a fixed set of the system parameters, entanglement can be produced just by adjusting the temperature difference between the reservoirs. The size of this entanglement, which is induced by temperature difference of reservoirs, increases as the spin-orbit parameter D increases. Also we find that, this environment induced entanglement can be improved if the qubit influenced by the weaker magnetic field is in contact with the hotter reservoir, i.e. indirect geometry of connection. In this case, the amount of asymptotic entanglement increases as D increases. Regardless of the geometry of connection, increasing D causes the appearance of entanglement in the larger regions of T_M-ΔT plane, therefore entanglement can exist in higher temperatures and temperature differences. Furthermore, increasing D enhances the amount of entanglement in these regions. We also show that the state of the system can be found in the maximally entangled state for the case of zero temperature reservoirs and large amount of the spin-orbit parameter.     

交错Dzyaloshinskii-Moriya相互作用对反铁磁Heisenberg链纠缠的影响

主要研究了具有交错Dzyaloshinskii-Moriya(DM)相互作用的反铁磁Heisenberg链的纠缠.基于 density-matrix renormalization group(DMRG)的数值计算表明,交错DM相互作用消除了系统在外磁场H=2处的二级量子相变,从而量子纠缠反常行为也随之消失;同时纠缠范围的发散也被消除,意味着该模型因子化点的消失.交错DM相互作用导致系统在任意强场下也不会达到铁磁饱和状态,从而保持着自旋纠缠.交错DM相互作用有利于通过外场调控纠缠程度和纠缠范 关键词： Dzyaloshinskii-Moriya相互作用 量子纠缠 量子相变 纠缠范围     

Thermal entanglement in the anisotropic Heisenberg model with Dzyaloshinskii-Moriya interaction in an inhomogeneous magnetic field

The thermal entanglement of a two-qubit anisotropic Heisenberg XXZ chain with Dzyaloshinskii-Moriya (DM) interaction in an inhomogeneous magnetic field was studied in detail. The effects of the DM parameter, external magnetic field (B), a parameter b which controls the inhomogeneity of B and the bilinear interaction parameters J_x = J_y ≠ J_z (the anisotropic case) on the concurrence (C) was formulated and studied in detail. The behaviors of the concurrences for the cases between (J = J_z = 1) and (J = -1,J_z = 1) and, (J = J_z = -1) and (J = 1,J_z = -1) at the ground state and at the thermal equilibrium are exactly the same. It was found that for the antiferromagnetic (AFM) case the entanglements persist to higher temperatures in comparison with the ferromagnetic (FM) case. In addition, the AFM case presents a special point at which the nonzero concurrences are all equal at some special temperatures. The further properties will be given in the text.     

外磁场下XY模型中两量子位热纠缠的性质及其调控研究

在海森堡XY模型中,为了统一研究均匀磁场和非均匀磁场对系统热纠缠的影响,在两个量子位分别施加独立可控的外磁场(B+b)和(B-b). 发现在均匀磁场和低温条件下的纠缠度有一个稳定的平台区并发生纠缠突变. 控制磁场不均匀度b和选择合适的材料就可以获得最有利的纠缠,并大大提高系统退纠缠的临界温度Tc. 调节磁场的B值,可以在更宽的温度范围内实现此体系的纠缠开关.     

具有Dzyaloshinskii-Moriya相互作用的一维随机量子XY模型中的纠缠特性

研究了一维随机量子XY自旋链中中心两量子位的纠缠特性,在该系统中引入了自旋间的交换耦合杂质、磁杂质和Dzyaloshinskii-Moriya相互作用,并且杂质满足高斯分布关系.通过数值计算,求出了自旋的关联函数和平均磁化强度,给出了Concurrence的解析表达式.结果表明:高斯分布和Dzyaloshinskii-Moriya相互作用对两量子位的纠缠有重要的影响,选择合适的交换耦合、外界磁场和Dzyaloshinskii-Moriya相互作用参数,可以控制和提高中心两量子位的纠缠.     

不同方向外磁场下海森堡自旋链的热纠缠

研究了两量子比特的海森堡XXX自旋链分别处于x方向和y方向均匀外磁场时系统的纠缠特性,并用负度N来度量。得到纠缠度N的解析表达式,并在此基础上进行数值计算。仔细讨论了磁场B、温度T和自旋耦合系数J对纠缠度N的影响。结果表明：纠缠度N会随着磁场|B|和温度T的增大而减小,但会随着自旋耦合系数J的增大而增大。另外,增大的J还会使临界磁场|Bc|和临界温度Tth变大。所以,我们可以通过调节B、T和J来控制热纠缠,这对固态系统中通过构建和选择参数调整系统的纠缠度具有一定的作用和意义。研究还发现,加在x方向均匀外磁场和加在y方向均匀外磁场对两量子比特的海森堡XXX自旋链的作用效果是一样的。     

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.     

Influence of dephasing on the entanglement teleportation via a two-qubit Heisenberg XYZ system

We study the entanglement dynamics of an anisotropic two-qubit Heisenberg XYZ system in the presence of intrinsic decoherence. The usefulness of such a system for performance of the quantum teleportation protocol T₀\mathcal{T}_0 and entanglement teleportation protocol T₁\mathcal{T}_1 is also investigated. The results depend on the initial conditions and the parameters of the system. The roles of system parameters such as the inhomogeneity of the magnetic field b and the spin-orbit interaction parameter D, in entanglement dynamics and fidelity of teleportation, are studied for both product and maximally entangled initial states of the resource. We show that for the product and maximally entangled initial states, increasing D amplifies the effects of dephasing and hence decreases the asymptotic entanglement and fidelity of the teleportation. For a product initial state and specific interval of the magnetic field B, the asymptotic entanglement and hence the fidelity of teleportation can be improved by increasing B. The XY and XYZ Heisenberg systems provide a minimal resource entanglement, required for realizing efficient teleportation. Also, in the absence of the magnetic field, the degree of entanglement is preserved for the maximally entangled initial states $\left| {\psi \left. {\left( 0 \right)} \right\rangle = \frac{1} {{\sqrt 2 }}\left( {\left| {\left. {00} \right\rangle \pm } \right|\left. {11} \right\rangle } \right)} \right.$\left| {\psi \left. {\left( 0 \right)} \right\rangle = \frac{1} {{\sqrt 2 }}\left( {\left| {\left. {00} \right\rangle \pm } \right|\left. {11} \right\rangle } \right)} \right.. The same is true for the maximally entangled initial states $\left| {\psi \left. {\left( 0 \right)} \right\rangle = \frac{1} {{\sqrt 2 }}\left( {\left| {\left. {01} \right\rangle \pm } \right|\left. {10} \right\rangle } \right)} \right.$\left| {\psi \left. {\left( 0 \right)} \right\rangle = \frac{1} {{\sqrt 2 }}\left( {\left| {\left. {01} \right\rangle \pm } \right|\left. {10} \right\rangle } \right)} \right., in the absence of spin-orbit interaction D and the inhomogeneity parameter b. Therefore, it is possible to perform quantum teleportation protocol T₀\mathcal{T}_0 and entanglement teleportation T₁\mathcal{T}_1, with perfect quality, by choosing a proper set of parameters and employing one of these maximally entangled robust states as the initial state of the resource.     

Entanglement in the anisotropic Heisenberg XYZ model with different Dzyaloshinskii-Moriya interaction and inhomogeneous magnetic field

We investigate the entanglement in a two-qubit Heisenberg XYZ system with different Dzyaloshinskii-Moriya (DM) interaction and inhomogeneous magnetic field. It is found that the control parameters (D_x, B_x and b_x) are remarkably different with the common control parameters (D_z, B_z and b_z) in the entanglement and the critical temperature, and these x-component parameters can increase the entanglement and the critical temperature more efficiently. Furthermore, we show the properties of these x-component parameters for the control of entanglement. In the ground state, increasing D_x (spin-orbit coupling parameter) can decrease the critical value b_xc and increase the entanglement in the revival region, and adjusting some parameters (increasing b_x and J, decreasing B_x and Δ) can decrease the critical value D_xc to enlarge the revival region. In the thermal state, increasing D_x can increase the revival region and the entanglement in the revival region (for T or b_x), and enhance the critical value B_xc to make the region of high entanglement larger. Also, the entanglement and the revival region will increase with the decrease of B_x (uniform magnetic field). In addition, small b_x (nonuniform magnetic field) has some similar properties to D_x, and with the increase of b_x the entanglement also has a revival phenomenon, so that the entanglement can exist at higher temperature for larger b_x.     

Teleportation and thermal entanglement in two-qubit Heisenberg X Y Z spin chain with the Dzyaloshinski-Moriya interaction and the inhomogeneous magnetic field

This paper studies the average fidelity of teleportation and thermal entanglement for a two-qubit Heisenberg X Y Z chain in the presence of both an inhomogeneous magnetic field and a Dzyaloshinski-Moriya interaction. It shows that for a fixed Dz, the increase of bz will broaden the critical temperature at the cost of decreasing the thermal entanglement. And it can modulate the inhomogeneous magnetic field and the Dzyaloshinski-Moriya interaction for the average fidelity of teleportation to be optimal.     

Thermal entanglement in a two-qubit Heisenberg XY chain with the Dzyaloshinskii--Moriya interaction

This paper investigates thermal entanglements of a two-qubit Heisenberg XY chain in the presence of the Dzyaloshinskii-Moriya anisotropic antisymmetric interaction. By the concept of concurrence, it is found that the effects of spin-orbit coupling on the entanglement are different from those of spin-spin model. The analytical expressions of concurrence are obtained for this model.