Dynamics of encrypted information in the presence of imperfect operations

The original dense coding protocol is achieved via quantum channel generated between a single Cooper pair and a cavity. The dynamics of the coded and decoded information are investigated for different values of the channel's parameters. The efficiency of this channel for coding and decoding information depends on the initial state settings of the Cooper pair. It is shown that, these information increase as the detuning parameter increases or the number of photons inside the cavity decreases. The coded and decoded information increase as the ratio of the capacities between the box and gate decreases. In the presence of imperfect operation, the sensitivity of the information to the phase error is much larger than the bit flip error.