  Quantum metrology theory has up to now focused on the resolution gains
obtainable thanks to the entanglement among N probes. Typically, a quadratic
gain in resolution is achievable, going from the 1/sqrt(N) of the central limit
theorem to the 1/N of the Heisenberg bound. Here we focus instead on quantum
squeezing and provide a unified framework for metrology with squeezing, showing
that, similarly, one can generally attain a quadratic gain when comparing the
resolution achievable by a squeezed probe to the best N-probe classical
strategy achievable with the same energy. Namely, here we give a quantification
of the Heisenberg squeezing bound for arbitrary estimation strategies that
employ squeezing. Our theory recovers known results (e.g.~in quantum optics and
spin squeezing), but it uses the general theory of squeezing and holds for
arbitrary quantum systems.
