The Quantum Dense Coding in a Two Atomic System Under the Non-Markovian Environment

The quantum dense coding in a two atomic system under the non-Markovian environment is investigated in detail. We mainly concentrate on the effects about the environment parameter Γ(or γ) and the purity r of the initial state on the dense coding capacity χ. It is found that the dense coding capacity χ is initially decreased and gradually trends to be a constant nonzero value with evolution of time for different environment parameter Γ(or γ). This constant value is determined the initial state and independent to the environment. In other word, environment noise only affects the process of quantum dense coding, but not affects the final result of dense coding capacity. The purity r of the initial state has a strong influence on the initial value of the χ. Besides, for one value r, dense coding capacity χ is decreased firstly, and then reaches a stable value for a long time, whatever the values of other parameters are, but when the purity r of the initial state increased, the initial value of dense coding capacity increased.