Coherent averaging

We investigate in detail a recently introduced coherent averaging scheme in terms of its usefulness for achieving Heisenberg limited sensitivity in the measurement of different parameters. In the scheme, N quantum probes in a product state interact with a quantum bus. Instead of measuring the probes directly and then averaging as in classical averaging, one measures the quantum bus or the entire system and tries to estimate the parameters from these measurement results. Combining analytical results from perturbation theory and an exactly solvable dephasing model with numerical simulations, we draw a detailed picture of the scaling of the best achievable sensitivity with N, the dependence on the initial state, the interaction strength, the part of the system measured, and the parameter under investigation. In particular, we identify the situations allowing one to reach Heisenberg-limited scaling of the sensitivity.