Photon-pair generation in a lossy microring resonator. II. Entanglement in the output mixed Gaussian squeezed state

In this work we examine the entanglement of the output signal-idler squeezed vacuum state in the Heisenberg picture as a function of the coupling and internal propagation loss parameters of a microring resonator. Using the log negativity as a measure of entanglement for a mixed Gaussian state, we examine the competitive effects of the transfer matrix that encodes the classical phenomenological loss, as well as the matrix that that incorporates the coupling and internal propagation losses due to the quantum Langevin noise fields required to preserve the unitarity of the composite system (signal-idler) and environment (noise) structure.