  Two path interferometry with coherent states and squeezed vacuum can achieve
phase sensitivities close to the Heisenberg limit when the average photon
number of the squeezed vacuum is close to the average photon number of the
coherent light. Here, we investigate the phase sensitivity of such states in
the presence of photon losses. It is shown that the Cramer-Rao bound of phase
sensitivity can be achieved experimentally by using a weak local oscillator and
photon counting in the output. The phase sensitivity is then given by the
Fisher information F of the state. In the limit of high squeezing, the ratio
(F-N)/N^2 of Fisher information above shot noise to the square of the average
photon number N depends only on the average number of photons lost, n_loss, and
the fraction of squeezed vacuum photons mu. For mu=1/2, the effect of losses is
given by (F-N)/N^2=1/(1+2 n_loss). The possibility of increasing the robustness
against losses by lowering the squeezing fraction mu is considered and an
optimized result is derived. However, the improvements are rather small, with a
maximal improvement by a factor of two at high losses.
