Coherently enhanced measurements in classical mechanics

Abstract In all quantitative sciences, it is common practice to increase the signal-to-noise ratio of noisy measurements by measuring identically prepared systems N times and averaging the measurement results. This leads to a scaling of the sensitivity as 1/√N, known in quantum measurement theory as the “standard quantum limit” (SQL). It is known that if one puts the N systems into an entangled state, a scaling as 1/N can be achieved, the socalled “Heisenberg limit” (HL), but decoherence problems have so far prevented implementation of such protocols for large N. Here we show that a method of coherent averaging inspired by a recent entanglement-free quantum enhanced measurement protocol is capable of achieving a sensitivity that scales as 1/N in a purely classical setup. This may substantially improve the measurement of very weak interactions in the classical realm, and, in particular, open a novel route to measuring the gravitational constant with enhanced precision.