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Chinese Physics B

Dense coding with a two-qubit Heisenberg XYZ chain under the influence of phase decoherence

Sulayiman Simayi, Aihemaiti Abulizi, Mushajiang Yaermaimaiti, Jiangtao Cai, Pan-Pan Qiao

Published May 1, 2011• 3 citations
Publisher

Abstract

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.

DOI
10.1088/1674-1056/20/5/050305

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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 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.
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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.
We investigate the entanglement dynamics of an anisotropic two-qubit Heisenberg XYZ system with Dzyaloshinskii-Moriya (DM) interaction in the presence of both inhomogeneity of the external magnetic field b and intrinsic decoherence which has been studied. The behavior of quantum correlation and the degree of entanglement between the two subsystems is quantified by using measurement-induced disturbance (MID), negativity (N) and Quantum Discord (QD), respectively. It is shown that in the presence of an inhomogeneity external magnetic field occur the phenomena of long-lived entanglement. It is found that the initial state is the essential role in the time evolution of the entanglement.