Phase estimation without a priori phase knowledge in the presence of loss

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Jan Kołodyński and Rafał Demkowicz-Dobrzański
Phys. Rev. A 82, 053804 (2010)

We find the optimal scheme for quantum phase estimation in the presence of loss when no a priori knowledge on the estimated phase is available. We prove analytically an explicit lower bound on estimation uncertainty, which shows that, as a function of the number of probes, quantum precision enhancement amounts at most to a constant factor improvement over classical strategies.