Sub-Heisenberg estimation of non-random phase-shifts

Abstract

We provide evidence that the uncertainty in detection of small and deterministic phase-shift deviations from a working point can be lower than the Heisenberg bound, for fixed finite mean number of photons. We achieve that by exploiting non-linearity of estimators and coherence with the vacuum.

Published version. Partially rewritten including further explanations and more numerical simulations. Updated references

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