Two-mode Gaussian product states in a Lossy Interferometer

The quantum Fisher information for a two-mode, Gaussian product state in an interferometer subject to photon loss is studied. We obtain the quantum Cramer-Rao bound on the achievable precision in phase estimation using such states. The scaling of the measurement precision with the mean photon number for such input product states is compared to the limited scaling for dual squeezed vacuum states and for dual squeezed, displaced vacuum states.