Quantum Dense Coding Properties Between Two Spatially Separated Atoms in Free Space

Quantum dense coding properties between two identical and spatially separated atoms in free space with different initial states is investigated. It shows that dense coding capacity χ experienced a sharp decline firstly and then gradually increased to be one steady value 1 with increasing Γ t . The realization of dense coding capacity χ is found to be strongly dependent on the initial states. It is worth noting that the initial pure state | e e 〉 is not useful for dense coding in this system, due to the dense coding capacity χ is always less than 1(a valid dense coding capacity satisfies χ > 1). Otherwise, for the initial entangled state and mixed state, one can obtain the valid dense coding capacity, the results show that one threshold value of t c is exists, and when t < t c the dense coding capacity is valid. Tuning the atomic distance between the two atoms slightly broaden the valid dense coding region and improve the value of t c . Decreasing the purity a of initial states not only broaden the region but also prolong the effective time where one can carry out the valid dense coding successfully.