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 of a two-qubit system with anisotropic couplings under nonuniform magnetic fields

This paper investigates bipartite entanglement of a two-qubit system with anisotropic couplings under an inhomogeneous magnetic field. This work is mainly to investigate the characteristics of a Heisenberg XYZ chain and obtains some meaningful results. By the concept of negativity, it finds that the inhomogeneity of magnetic field may induce entanglement and the critical magnetic field is independent of J_z. The inhomogeneous magnetic field can increase the value of critical magnetic field B_c. It also finds that the magnetic field not only suppresses the entanglement but also can induce it to revival for some time.     

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.     

Teleportation via thermally entangled states of a two-qubit Heisenberg XXZ chain

We investigate quantum teleportation as a tool to study the thermally entangled state of a twoqubit Heisenberg XXZ chain.Our work is mainly to investigate the characteristics of a Heisenberg XXZ chain and get some analytical results of the fully entangled fraction.We also consider the entanglement teleportation via a two-qubit Heisenberg XXZ chain.     

Teleportation via thermally entangled states of a two-qubit Heisenberg XXZ chain

We investigate quantum teleportation as a tool to study the thermally entangled state of a two-qubit Heisenberg XXZ chain. Our work is mainly to investigate the characteristics of a Heisenberg XXZ chain and get some analytical results of the fully entangled fraction. We also consider the entanglement teleportation via a two-qubit Heisenberg XXZ chain.     

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.     

Effect of spin-orbit interaction on entanglement of two-qutrit Heisenberg XYZ systems in an inhomogeneous magnetic field

We investigate the properties of spin-orbit interaction in the ground state and thermal entanglement of a two-qutrit Heisenberg XYZ system in the presence of an inhomogeneous magnetic field. Using negativity as entanglement measure, we give the dependence of entanglement on each parameter in detail. The result shows that one can get appropriate entanglement by adjusting the magnetic field, Dzyaloshinskii-Moriya interaction and anisotropy parameter simultaneously.     

Bipartite entanglement in spin-1/2 Heisenberg model

The bipartite entanglement of the two- and three-spin Heisenberg model was investigated by using the concept of negativity. It is found that for the ground-state entanglement of the two-spin model, the negativity always decreases as B increases if Δ<γ－1, and it may keep a steady value of 0.5 in the region of B2－γ²]^1/2 if Δ>γ－1, while for that of the three-spin model, the negativity exhibits square wave structures if γ=0 or Δ=0. For thermal states, there are two areas showing entanglement, namely, the main region and the sub-region. The main region exists only when Δ>Δ_c (Δ_c=γ－1 and (γ²－1)/2 for the 2- and 3-spin model respectively) and extends in terms of B and T as Δ increases, while the sub-region survives only when γ≠0 and shrinks in terms of B and T as Δ increases.     

Quantum Teleportation Through a Two-Qubit Heisenberg XXZ Chain

We consider a two-qubit Heisenberg XXZ chain as a resource for quantum teleportation via the standard teleportation protocol To. The effects of anisotropic on teleportation fidelity and entanglement are studied in detail. We find anisotropic not only improves the criticM temperature Tc and criticM magnetic field Bc, beyond which quantum teleportation is inferior to classicM communication protocol, but also enhances the fidelity for fixed magnetic field B and temperature T. For entanglement teleportation, the effects of magnetic field on average fidelity and output entanglement are studied.     

Effect of spin-orbit interaction on entanglement of two-qutrit Heisenberg XYZ systems in an inhomogeneous magnetic field

We investigate the properties of spin-orbit interaction in the ground state and thermal entanglement of a two-qutrit Heisenberg XYZ system in the presence of an inhomogeneous magnetic field. Using negativity as entanglement measure, we give the dependence of entanglement on each parameter in detail. The result shows that one can get appropriate entanglement by adjusting the magnetic field, Dzyaloshinskii-Moriya interaction and anisotropy parameter simultaneously.     

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.     

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 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.     

Entanglement in spin-1 Heisenberg <Emphasis Type="Italic">XY</Emphasis> chain

We investigated the quantum entanglement in spin-1 Heisenberg XY chain for two-spin-qutrit and multi-particle systems. As a measure of the entanglement, the negativity of this state was analyzed as a function of the temperature and the magnetic field. We gave some numerical results and discussed them in detail. We found that the negativity increases monotonously with the coupling constants |J ₁| and |J ₂|, and it showed a symmetry with respect to the point of J ₁ = 0 and J ₂ = 0. In addition to the above features, there is evidence that the critical temperature is independent of the length of the chain.     

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.     

Quantum correlations in a two-qubit anisotropic Heisenberg XYZ chain with uniform magnetic field

Quantum correlations in an anisotropic Heisenberg XY Z chain is investigated by use of concurrence C and measurement-induced disturbance(MID). We show that the behaviors of the MID are remarkably different from the concurrence. Firstly, it is shown that there is a revival phenomenon in the concurrence but not in the MID, which is suitable for both the ground state case and the finite temperature case. Based on the analysis of the ground-state C and MID structures,we illustrate the reason why the ground-state MID does not show a revival phenomenon in detail. Then we explore different effects of the external and self parameters on entanglement and MID behaviors. It can be shown that the region of MID is evidently larger than the case of concurrence, and that the concurrence signals a quantum phase transition even at finite T while MID does not. Cases where the concurrence finally maintains one nonzero constant value regardless of the value of the variable B for a constant Jz, while MID decreases monotonously to zero with increasing B. We also show that if B can take a proper range of values, the concurrence decreases with the improvement of the anisotropic parameter γ, whereas an opposite effect for MID behaviors is presented.     

Bipartite entanglement in spin-1/2Heisenberg model

The bipartite entanglement of the two-and three-spin Heisenberg model was investigated by using the concept of negativity.It is found that for the ground-state entanglement of the two-spin model,the negativity always decreases as B increases if A Δ＜y-1,and it may keep a steady value of 0.5in the region of B＜J[(Δ+1)2-y2]1/2if Δ＞y-1,while for that of the three-spin model,the negativity exhibits square wave structures if y=0 or Δ=0.For thermal states,there are two areas showing entanglement,namely,the main region and the sub-region.The main region exists only when Δ＞Δc(Δc1=and(y2-1)/2for the 2-and 3-spin model respectively)and extends in terms of B and T as Δ increases,while the sub-region survives only when y≠0 and shrinks in terms of B and T as Δ increases.     

Bipartite and Tripartite Entanglement in a Three-Qubit Heisenberg Model

The bipartite and tripartite entanglement in a three-qubit Heisenberg XY model with a nonuniform magnetic field is studied. There are two or four peaks in the concurrence of the bipartite entanglement when the amplitudes of the magnetic fields are. differently distributed between the three qubits. It is very interesting to note that there is no tangle of tripartite entanglement between the three qubits when the amplitudes of the magnetic fieMs are varied. However, the variation of the magnetic field direction can induce the tangle. The tangle is periodic about the angle between the magnetic field and the z axis of the spin.