  The quantum Fisher information (QFI) bounds the sensitivity of a quantum
measurement, heralding the conditions for quantum advantages. We aim to find
conditions at which quantum advantage can be realized in single-parameter phase
sensing with nonlinear interferometers. Here, we calculate analytical
expressions for the QFI of nonlinear interferometers under lossy conditions and
with coherent-state seeding. We normalize the results based on the number of
photons going through the phase-inducing element, which eliminates some of the
previously declared metrological advantages. We analyze the performance of
nonlinear interferometers in a variety of geometries and robustness of the
quantum advantage with respect to internal and external loss through direct
comparison with a linear interferometer. We find the threshold on the internal
loss at which the quantum advantage vanishes, specify when and how much
coherent-state seeding optimally counters internal loss, and show that a
sufficient amount of squeezing confers to the quantum advantages robustness
against external loss and inefficient detection.
