  We consider the problem of estimating multiple phases using a multi-mode
interferometer. In this setting we show that while global strategies with
multi-mode entanglement can lead to high precision gains, the same precision
enhancements can be obtained with mode-separable states and local measurements.
The crucial resource for quantum enhancement is shown to be a large number
variance in the probe state, which can be obtained without any entanglement
between the modes. This has important practical implications because local
strategies using separable states have many advantages over global schemes
using multi-mode-entangled states. Such advantages include a robustness to
local estimation failure, more flexibility in the distribution of resources,
and comparatively easier state preparation. We obtain our results by analyzing
two different schemes: the first uses a set of interferometers, which can be
used as a model for a network of quantum sensors, and the second looks at
measuring a number of phases relative to a reference, which is concerned
primarily with quantum imaging.
