Title: Quantum interferometry in multi-mode systems,
Abstract: We consider the situation when the signal propagating through each arm of an
interferometer has a complicated multi-mode structure. We find the relation
between the particle-entanglement and the possibility to surpass the shot-noise
limit of the phase estimation. Our results are general---they apply to pure and
mixed states of identical and distinguishable particles (or combinations of
both), for a fixed and fluctuating number of particles. We also show that the
method for detecting the entanglement often used in two-mode system can give
misleading results when applied to the multi-mode case.