In this paper, the master equation for the coupled lossy waveguides is solved using the thermofield dynamics(TFD) formalism. This formalism allows the use of the underlying symmetry algebras SU(2) and SU(1,1), associated with the Hamiltonian of the c
oupled lossy waveguides,to compute entanglement and decoherence as a function of time for various input states such as NOON states and thermal states.
