  The quantum Cram\'er-Rao bound (QCRB) sets a fundamental limit for the
measurement of classical signals with detectors operating in the quantum
regime. Using linear-response theory and the Heisenberg uncertainty relation,
we derive a general condition for achieving such a fundamental limit. When
applied to classical displacement measurements with a test mass, this condition
leads to an explicit connection between the QCRB and the Standard Quantum Limit
which arises from a tradeoff between the measurement imprecision and quantum
backaction; the QCRB can be viewed as an outcome of a quantum non-demolition
measurement with the backaction evaded. Additionally, we show that the test
mass is more a resource for improving measurement sensitivity than a victim of
the quantum backaction, which suggests a new approach to enhancing the
sensitivity of a broad class of sensors. We illustrate these points with laser
interferometric gravitational wave detectors.
