Quantum entanglement of decohered two-mode squeezed states in absorbing and amplifying environment

We investigate the properties of quantum entanglement of two-mode squeezed states interacting with linear baths with general gain and loss parameters. By explicitly solving for ρfrom the master equation, we determine analytical expressions of eigenvalues and eigenvectors of ρ^{T_A} (the partial transposition of density matrix ρ). In Fock space, ρ^{T_A} is shown to maintain a block diagonal structure as the system evolves. In addition, we discover that the decoherence induced by the baths would break the degeneracy of ρ^{T_A}, and leads to a novel set of eigenvectors for the construction of entanglement witness operators. Such eigenvectors are shown to be time-independent, which is a signature of robust entanglement of two-mode squeezed states in the presence of noise.