Entanglement structure of two-mode squeezed states in absorbing and amplifying environment

We examine the structure of entanglement for two-mode squeezed states interacting with symmetric linear baths [1]. In Fock space, $\rho^{T_A}$ is observed to be maintaining a block diagonal form as the system evolves. We explicitly obtain the eigenvalues and eigenvectors of $\rho^{T_A}$ (the partial transposition of density matrix $\rho$) as a function of time. The decoherence induced by the baths are shown to destroy the degeneracy of $\rho^{T_A}$, leading to a set of eigenvectors for the construction of entanglement witness operators. We prove that the eigenvectors are time-independent, which is an indicator for the robustness of entanglement of two-mode squeezed states in the presence of noise. \newline \noindent [1] Phoenix S. Y. Poon and C. K. Law, Phys. Rev. A \textbf{76}, 012333 (2007).