Unification of Metrological Powers of Nonclassical Single-Mode States

Nonclassical states enable metrology with 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 resources. 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 time (phase shifts). In this presentation, I will answer this question for all single-mode states, both for local and distributed metrology using an arbitrary linear network that achieves this maximal precision. I will show 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.