  Nonclassical states enable metrology with a precision beyond that possible
with classical physics. Both for practical applications and to understand
non-classicality as a resource, it is useful to know the maximum quantum
advantage that can be provided by a nonclassical state when it is combined with
arbitrary classical states. This advantage has been termed the "metrological
power" of a quantum state. A key open question is whether the metrological
powers for the metrology of different quantities are related, especially
metrology of force (acceleration) and phase shifts (time). Here we answer this
question for all single-mode states, both for local and distributed metrology,
by obtaining complete expressions for the metrological powers for the metrology
of essentialy any quantity (any single-mode unitary transformation), as well as
the linear networks that achieve this maximal precision. This shows that the
metrological powers for all quantities are proportional to a single property of
the state, which for pure states is the quadrature variance, maximized over all
quadratures.
