Quantum entanglement of symmetrically decohered two-mode squeezed states in an absorbing and amplifying environment
Phoenix S. Y. Poon, C. K. Law · Physical Review A · 2007
We investigate the properties of quantum entanglement of two-mode squeezed states interacting with symmetric linear baths with general gain and loss parameters. By explicitly solving for $\ensuremath{\rho}$ from the master equation, we determine analytical expressions of eigenvalues and eigenvectors of ${\ensuremath{\rho}}^{{T}_{A}}$ (the partial transposition of density matrix $\ensuremath{\rho}$). In Fock space, ${\ensuremath{\rho}}^{{T}_{A}}$ 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 ${\ensuremath{\rho}}^{{T}_{A}}$, and leads to a 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.