Optimal Dense Coding in a Two-qubit Heisenberg XXZ Model with Decoherence

Optimal dense coding of a two-qubit anisotropic Heisenberg XXZ model under decoherence is investigated with the Werner state as the initial state. With the time evolution, the dense coding capacity χ oscillates firstly, and then reaches a stable value 1 in the long time limit, whatever the values of other parameters are. Our results imply that the purity r of the initial state have a strong influence on the initial value of the optimal dense coding capacity. When the purity r of the initial state increase, the initial value of dense coding capacity increase. Besides, the coupling coefficient and Dzyaloshinski-Moriya(DM) both have strong influence on the frequency of the oscillation and the area of t that the optimal dense coding is feasible(tf). Interestingly, the decoherence rate γ can strongly affect the dense coding capacity. With the decreasing of γ, the area of tf(which will make the dense coding capacity greater than 1) becomes more wider. When γ = 0, it will still allows a valid dense coding. So we can adjust the parameters to get a optimal dense coding.