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Physica Scripta

Effect of Dzyaloshinskii–Moriya anisotropic antisymmetric interaction on optimal dense coding

Liang Qiu, An Min Wang, Xiao Qiang Su, XIAO SAN MA

Published Dec 19, 2008• 3 citations
Publisher

Abstract

We study optimal dense coding in the two-qubit and two-qutrit Heisenberg XXX models with Dzyaloshinskii–Moriya anisotropic antisymmetric interaction (DM interaction). Both the DM interaction and the coupling parameter can enhance the maximum dense coding capacity for high temperature. For low temperature, in the two-qutrit system, the coupling parameter still enhances the maximum dense coding capacity, while the DM interaction weakens the capacity of the channel for dense coding.

DOI
10.1088/0031-8949/79/01/015005

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Modern Physics Letters B•Feb 20, 2010•0 citations
We study optimal dense coding in the two-qubit and two-qutrit Heisenberg XXX models with Dzyaloshinskii–Moriya anisotropic antisymmetric interaction (DM interaction). Both the DM interaction and the coupling parameter can enhance the maximum dense coding capacity for high temperature. For low temperature, in the two-qutrit system, the coupling parameter still enhances the maximum dense coding capacity, while the DM interaction weakens the capacity of the channel for dense coding.
We investigate the effects of different components of the Dzyaloshinskii—Moriya (DM) anisotropic antisymmetric interaction on optimal dense coding with a two-qubit Heisenberg XXZ chain in the presence and in the absence of external magnetic fields. The anisotropic coupling parameter Δ, isotropic coupling parameter J , and the DM interaction parameters are found to be effective for optimal dense coding, while the magnetic field turns out to be destructive. Moreover, the results show that the case of antiferromagnetic (AFM) is more ideal for optimal dense coding than the case of ferromagnetic (FM) in general. In the case of AFM, by comparison of the two cases with the same fixed x - and z -component parameters of DM interaction ( D x and D z ), the appropriate model for optimal dense coding is indicated for the different value intervals of Δ. Comparison of the effects of D z and D x on optimal dense coding is made and their dominant regions are clarified.
Optimal dense coding with thermal entangled states of a two-qubit anisotropic XXZ model and a Heisenberg model with Dzyaloshinskii–Moriya (DM) interactions is studied in this paper. The DM interaction is another kind of anisotropic antisymmetric exchange interaction. The effects of these two kinds of anisotropies on dense coding are studied in detail for both the antiferromagnetic and ferromagnetic cases. For the two models, I give the conditions that the parameters of the models have to satisfy for a valid dense coding. I also found that even though there is entanglement, it is unavailable for our optimal dense coding, which is the same as entanglement teleportation.
By solving the Milburn equation, we investigate the properties of optimal channel capacity for the quantum dense coding via a two-qubit Heisenberg spin system with Dzyaloshinskii-Moriya (DM) interaction in the presence of intrinsic decoherence. The influences of different DM interactions, different initial states, anisotropic coupling parameters, and intrinsic decoherence on optimal coding capacity are analyzed in detail. It is found that the initial state of the system affects optimal coding capacity greatly, whose dependent parameters are not identical for different types of initial states. When the system is initially in the form of the nonmaximally entangled state cft| {01} ightangle + dft| {10} ightangle , a weak z-component DM interaction can enhance the value of optimal coding capacity as compared with the value without DM interaction, and the phase decoherence effect can suppress the oscillation of optimal coding capacity and make the capacity decrease to a stable value for the long-time evolution. It is also found that under the influence of intrinsic decoherence, the optimal transmission capacity of dense coding can keep an ideal maximal value of 2 by choosing the proper initial maximally entangled state. Moreover, no matter from which direction the DM interaction is introduced, the optimal coding capacity via the two-qubit Heisenberg spin system is always larger than the transmission capacity of any classical communication.
We investigate the joint effects of phase decoherence, Dzyaloshinskii-Moriya (DM) interaction and inhomogeneity of the external magnetic field ( b ) on dense coding in a two-qubit anisotropic Heisenberg XYZ spin chain. Analytical expressions are obtained for the dense coding capacity. It is found that valid dense coding is always possible with this model when the system is initially prepared in the maximum entangled state. Moreover, optimal dense coding can be implemented for this initial state as long as the mean spin-spin coupling constant J + of the XY plane is larger than b and the DM interaction despite the intrinsic decoherence. Non-maximal entangled initial states are found to be undesirable for dense coding with this model.
Mutual information and swap operation in the two-qubit Heisenberg model with the Dzyaloshinskii–Moriya (DM) anisotropic antisymmetric interaction are investigated. It is found that the mutual information I of such a quantum channel is sensitive to the initial conditions and declines with increase in temperature. The DM interaction can lead to higher mutual information, especially for the ferromagnetic case. The entanglement quality of input states cannot enhance the mutual information of the quantum channel. When the DM interaction is large, the mutual information will have the maximum value of 2 for a non-entangled input state, but it is 1 for a maximally entangled input state. It is also shown that the swap operation can be implemented for some kinds of DM coupling. The conditions of the DM coupling under which the swap operation is feasible are established.
Thermal entanglement of a two-qubit Heisenberg XXZ chain in the presence of different Dzyaloshinskii–Moriya (DM) anisotropic antisymmetric interactions and entanglement teleportation using two independent Heisenberg chains as quantum channel are investigated. It is found that the anisotropic coupling coefficient Jz (z-component exchange constant) and DM interactions can excite the entanglement, and x-component DM interaction Dx has a more remarkable influence than the z-axis DM interaction Dz for exchange constant J > 0 (antiferromagnetic) case, which is contrary to coupling coefficient J < 0 (ferromagnetic) case. The output entanglement and fidelity increase with increasing z-axis coupling parameter Jz for both the antiferromagnetic J > 0 case and ferromagnetic J < 0 case. By introducing the different DM interactions, it is superior to teleportate initial state by using the Dz interaction in the model for J > 0 case. But for J < 0 case, the Dx interaction is better, and the output concurrence and fidelity can reach the maximum value 1 with suitable Dx.