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Abstract: We give the optimal bounds on the phase-estimation precision for mixedGaussian states in the single-copy and many-copy regimes. Specifically, wefocus on displaced thermal and squeezed thermal states. We find that while fordisplaced thermal states an increase in temperature reduces the estimationfidelity, for squeezed thermal states a larger temperature can enhance theestimation fidelity. The many-copy optimal bounds are compared with the minimumvariance achieved by three important single-shot measurement strategies. Weshow that the single-copy canonical phase measurement does not always attainthe optimal bounds in the many-copy scenario. Adaptive homodyning schemes doattain the bounds for displaced thermal states, but for squeezed states theyyield fidelities that are insensitive to temperature variations and are,therefore, sub-optimal. Finally, we find that heterodyne measurements performvery poorly for pure states but can attain the optimal bounds for sufficientlymixed states. We apply our results to investigate the influence of losses in anoptical metrology experiment. In the presence of losses squeezed states ceaseto provide Heisenberg limited precision and their performance is close to thatof coherent states with the same mean photon number.

Autor: M. Aspachs, J. Calsamiglia, R. Munoz-Tapia, E. Bagan


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