Partial Teleportation of Entanglement Through Natural Thermal Entanglement in Two-Qubit Heisenberg XXX Chain

Natural thermal entanglement between two qubits with XXX Heisenberg interaction is studied. For the antiferromagnet, increasing coupling strength or decreasing temperature under critical point increases the entanglement. Based on the thermal entanglement as quantum channel, entanglement and information of an input entangled state are transferred via partial teleportation. We find that the entanglement transferred will be lost du~ing the process, and for the entanglement fidelity the partial teleportation is superior to classical communication as concurrence of entangled channel beyond 1/4. We show that both correlation information in input entangled state and individual information of the teleported particle are linearly dissipated. With more entanglement in quantum channel, more entanglement and correlation information can be transferred.

Ground-State and Thermal Entanglement in Three-Spin Heisenberg-XXZ Chain with Three-Spin Interaction

The entanglement properties of a three-spin X X Z Heisenberg chain with three-spin interaction are studied by means of concurrence of pairwise entanglement. We show that ground-state pairwise entanglement, pairwise thermal entanglement, or quantum phase transition is not present in antiferromagnetic spin chain. For the ferromagnetic case, quantum phase transition takes place at A = 1 for anisotropic interaction and at some values of three-spin coupling strength, and pairwise thermal entanglement increases when the value of J/T increases and with anisotropic interaction and three-spin interaction decrease. In addition, we find that increasing the anisotropic interaction and the three-spin interaction will decrease critical temperature.

Pairwise thermal entanglement in a three-qubit Heisenberg XX model with a nonuniform magnetic field and Dzyaloshinski-Moriya interaction

Pairwise thermal entanglement in a three-qubit Heisenberg XX model is investigated when a nonuniform mag- netic field and the Dzyaloshinski-Moriya interaction are included. We find that the nonuniform magnetic field and Dzyaloshinski-Moriya interaction are the more efficient control parameters for the increase of entanglement and critical temperature. For both the nearest neighbour sites and the next nearest neighbour sites, the magnetic field can induce entanglement to a certain extent and the Dzyaloshinski-Moriya interaction can enhance the entanglement to a stable value. The steady value of the nearest neighbour site entanglement C12 is larger than the next nearest neighbour site entanglement C13. An interesting phenomenon is that the entanglement curve of C12 appears a peak value when the Dzyaloshinski-Moriya interaction is considered in a nonuniform magnetic field.

Thermal entanglement in molecular spin rings

The thermal entanglement in the triangular molecular spin ring with Dzyaloshinskii-Moriya interaction is studied. The concurrences of arbitrary two spins of the triangular molecular spin ring for various cases are evaluated. The tendency of the concurrence with Dzyaloshinskii-Moriya interaction and temperature is analysed and discussed. We note that the concurrence arrives at its maximum in the regime with the large Dzyaloshinskii-Moriya interaction and low temperature, and gradually decreases to zero with the increase of temperature. The concurrence has different features for the ferromagnetic and antiferromagnetic cases. For completeness, we also numerically calculate the concurrence of spin rings with N 〉 3 spins and analyse their behaviours.

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 XYZ 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 of a Two-Qubit XXZ Heisenberg Chain with Dzialoshinski-Moriya Interaction

The effect of DziaJoshinski-Moriya （DM） interaction on thermal entanglement of a two-qubit XXZ spin chain in a homogenous magnetic field is investigated. It is found that the DM interaction can enhance thermal entanglement. When D is large enough, the entanglement can exist for larger temperatures and strong magnetic field.

Thermal entanglement of the Ising Heisenberg diamond chain with Dzyaloshinskii Moriya interaction

We investigate the thermal entanglement in a spin-l/2 Ising-Heisenberg diamond chain, in which the vertical Heisen- berg spin dimers alternate with single Ising spins. Due to the fact that the Dzyaloshinskii-Moriya （DM） interaction con- tributes to unusual and interesting magnetic properties in actual materials, and moreover it plays a significant role in the degree of the entanglement of the Heisenberg quantum spin systems, we focus on the effects of different DM interactions, including Dz and Dx, on the thermal entanglement of the Heisenberg spin dimer. The concurrence, as a measure of spin dimer entanglement, is calculated for different values of exchange interactions, DM interaction, external magnetic field, and temperature. It is found that the critical temperature and the critical magnetic field corresponding to the vanishing of entanglement increase with DM interaction, and the entanglement revival region gets larger by increasing DM interac- tion, thus DM interaction favors the formation of the thermal entanglement. It is observed that different DM interaction parameters （Dz and Dx） have remarkably different influences on the entanglement. Different from the case Dz, there is the non-monotonic variation of the concurrence with temperature in the case Dx, and additionally the DM interaction Dx can induce the entanglement near zero temperature in the case that the antiferromagnetic Ising-type interaction constant is larger than the antiferromagnetic Heisenberg interaction constant. It is also shown that for the same value of DM interaction the critical magnetic field of the case Dx is larger than that of the case Dz.

Thermal entanglement in two-qutrit spin-1 anisotropic Heisenberg model with inhomogeneous magnetic field

The thermal entanglement of a two-qutrit spin-1 anisotropic Heisenberg XXZ chain in an inhomogeneous magnetic field is studied in detail. The effects of the external magnetic field （B）, a parameter b which controls the inhomogeneity of B, and the bilinear interaction parameters Jx = Jy ≠ Jz on the thermal variation of the negativity are studied in detail. It is found that negativity N decreases when the values of magnetic field, inhomogeneity b and temperature are increasing. In addition, N remains at higher temperatures for higher values of Jz and lower values of B and b.

Thermal entanglement of the spin-1 Ising-Heisenberg diamond chain with biquadratic interaction

We investigate the thermal entanglement of the spin-1 Ising-Heisenberg diamond chain, which can be regarded as a theoretical model for the homometallic molecular ferrimagnet [Ni_3（C_4H_2O_4）_2-（μ_3-OH）_2（H_2O）_4]n ·（2H_2O）n. Two cases,i.e., the isotropic Heisenberg（Ising-XXX） coupling model and anisotropic Heisenberg（Ising-XXZ） coupling model, are discussed respectively. The negativity is chosen as the measurement of the thermal entanglement. By means of the transfermatrix approach, we focus on the effects of biquadratic interaction parameters on the negativity of the infinite spin-1 Ising-Heisenberg diamond chain. In the Ising-XXX coupling model, it is shown that for the case with ferromagnetic coupling the thermal entanglement can be induced by the biquadratic interaction, but the external magnetic field will suppress the occurrence of the entanglement induced by the biquadratic interaction. In the Ising-XXZ coupling model,for the case with antiferromagnetic coupling, due to the biquadratic interaction the effect of the anisotropy parameter on the entanglement will be suppressed at near-zero temperature. Moreover, the biquadratic interaction makes the threshold temperature increase. The effects of the external magnetic field on the thermal entanglement are also discussed, and it is observed that the entanglement revival phenomena exist in both models considered.

Effects of Different Spin-Spin Couplings and Magnetic Fields on Thermal Entanglement in Heisenberg XYZ Chain

The effects of spin-spin interaction on thermed entanglement of a two-qubit Heisenberg XYZ model with different inhomogeneous magnetic fields are investigated. It is shown that the entanglement is dependent on the spin-spin interaction and the inhomogeneous magnetic fields. The larger the Ji （i-axis spin-spin interaction）, the higher critical value the Bi （i-axis uniform magnetic field） has. Moreover, in the weak-field regime, the larger Ji corresponds to more entanglement, while in the strong-field regime, different Ji correspond to the same entanglement. In addition, it is found that with the increase of Ji, the concurrence can approach the maximum value more rapidly for the smaller Bi, and can reach a larger value for the smaller bi （i-axis nonuniform magnetic field）. So we can get more entanglement by increasing the spin-spin interaction Ji, or by decreasing the uniform magnetic field Bi and the nonuniform magnetic field hi.

Thermal entanglement in a spin-1/2 Ising-Heisenberg butterfly-shaped chain with impurities

We investigate the effect of impurities on the thermal entanglement in a spin-1/2 Ising-Heisenberg butterfly-shaped chain,where four interstitial Heisenberg spins are localized on the vertices of a rectangular plaquette in a unit block.By using the transfer-matrix approach,we numerically calculate the partition function and the reduced density matrix of this model.The bipartite thermal entanglement between different Heisenberg spin pairs is quantified by the concurrence.We also discuss the fluctuations caused by the impurities through the uniform distribution and the Gaussian distribution.Considering the effects of the external magnetic field,temperature,Heisenberg and Ising interactions as well as the parameter of anisotropy on the thermal entanglement,our results show that comparing with the case of the clean model,in both the twoimpurity model and the impurity fluctuation model the entanglement is more robust within a certain range of anisotropic parameters and the region of the magnetic field where the entanglement occurred is also larger.

Thermal Entanglement in Lipkin-Meshkov-Glick Model

We investigate the thermal entanglement in the Lipkin-Meshkov-G1ick （LMG） model which consists of spin-1/2 particles with XXZ-type exchange interactions between any pair of them. The ferromagnetic （FM） and antiferromagnetic （AFM） cases are completely analyzed at both finite temperature and zero temperature. According to the results obtained by accurate numerical calculation, several interesting physic phenomena and characteristics of thermal entanglement in the LMG model are found. Not only do we evaluate the entanglement of the LMG model, but also discover the correlations between macroscopic physical quantities and thermal entanglement.

Thermal entanglement and teleportation of a thermally mixed entangled state of a Heisenberg chain through a Werner state

The thermal entanglement and teleportation of a thermally mixed entangled state of a two-qubit Heisenberg XXX chain under the Dzyaloshinski Moriya （DM） anisotropic antisymmetric interaction through a noisy quantum channel given by a Werner state is investigated. The dependences of the thermal entanglement of the teleported state on the DM coupling constant, the temperature and the entanglement of tbe noisy quantum channel are studied }n detail for both the ferromagnetic and the antiferromagnetic cases. The result shows that a minimum entanglement of the noisy quantum channel must be provided in order to realize the entanglement teleportation. The values of fidelity of the teleported state are also studied for these two cases. It is found that under certain conditions, we can transfer an initial state with a better fidelity than that for any classical communication protocol.

Tunable thermal entanglement in an effective spin-star system using coupled microcavities

We theoretically explore the possibility of realizing controllable thermal entanglement of effective spins in a four-qubit anisotropic Heisenberg XXZ coupling spin-star system constructed by coupled microcavities. We analyse the dependence of thermal entanglement in this system on temperature, inhomogeneity of the magnetic field, and anisotropy, which can be readily tuned via the external laser fields. The peculiar characteristic and the full controllability of the thermal entanglement are demonstrated to be useful for quantum information processing.

Thermal Entanglement of an XY Two-Qutrit Spin Chain with Dzialoshinski—Moriya Interaction

The effect of Dzialoshinski-Moriya(DM)interaction on thermal entanglement of an XY two-qutrit spinchain is investigated.We find that DM interaction and the anisotropy parameter can enhance quantum thermal entanglementto a maximal value individually.However,when both of them take large values,the entanglement is notenhanced,but is destroyed.Our analysis will shed some light on the understanding of the effect of the DM interactionon thermal entanglement of an XY two-qutrit spin chain.

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.

Thermal Entanglement in the Pure Dzyaloshinskii-Moriya Model with Magnetic Field

We investigate the effects of the directions of Dzyaloshinskii Moriya （DM） interaction and magnetic field on the thermal entanglement in the pure DM model. It is found that when the Hamiltonian is H1 = D. （σ1 ＋σ2） ＋B.σ1, the entanglement can reach its maximum if the directions of the magnetic field and the DM vector are parallel. In addition, when the Hamiltonian is H2 = D @ （σ1 σ2） ＋ B. （σ1 ＋ σ2）, if the directions of the magnetic field and the DM vector are perpendicular in a high magnetic field, or their directions are parMlel in a weak magnetic field, the entanglement can also reach its maximum. Thus the entanglement can be enhanced by adjusting the direction of the external magnetic field, and this is feasible within the current experimental technology.

Thermal Entanglement in Two-Qutrit Heisenberg XX Chain with Different Dzyaloshinskii-Moriya Interaction and Nonuniform Magnetic Field

The effects of the different Dzyaloshinskii-Moriya （DM） interaction on thermal entanglement of a two-qutrit Heisenberg XX spin chain in a nonuniform magnetic field are investigated. Our results imply that the x-component DM interaztion plays a central role in enhancing quantum entanglement and it has a higher critical temperature than the z-component DM interaction. The entanglement can be tunable controlled by changing the multiple of the magnetic fields B1 and B2. Also we found that different DM interaction are competitive to each other in some conditions.

Entanglement and Teleportation via Thermally Entangled State of Anisotropic Heisenberg XYZ Chain with Inhomogeneous External Magnetic Field

In this paper we study the entanglement in a two-qubit spin in the XYZ model, and teleport a two-qubit entangled state using this spin chain in the condition of the thermal equilibrium as a quantum channel. We investigate the effects of the interaction of z-component Jz, the inhomogeneous magnetic field b, the anisotropy γ and the temperature T on the entanglement and fidelity. In order to characterize the quality of the teleported state, we research the average fidelity Fα. High average fidelity of the teleportation is obtained when the temperature is very low. Under some condition, we also find that when innomogeneity increases to a certain value, the average fidelity can exhibit a larger revival than that for less values of b.

Quantum Phase Transition and Thermal Entanglement in the Isotropic XXX Model

We investigate the quantum phase transition （OPT） and the pairwise thermal entanglement in the three- qubit Heisenberg XXX chain with Dzyaloshinskii Moriya （DM） interaction under a magnetic field. The ground states of the system exist crossing points, which shows that the system exhibits a Q, PT. At a given temperature, the entanglement undergoes two sudden changes （platform-like behavior） as the DM interaction or external magnetic field increases. This special property can be used as the entanglement switch, which is also influenced by the temperature. We can modulate the DM interaction or external magnetic field to control the entanglement switch.