Evolution of a two-mode squeezed vacuum in the amplitude dissipative channel

For the first time we derive the dissipating result of an initial two-mode squeezed pure vacuum state passing through a two-mode amplitude dissipative channel described by the direct product of two independent single-mode master equations.Although these two master equations do not mix the two modes (there is no coupling between them),since the two-mode squeezed state is simultaneously an entangled state,the final state which emerges from passing this channel is a two-mode mixed density operator.The compact expression of the outcoming state is obtained,which manifestly shows that as time evolves,the squeezing effect decreases.