Uncertainty limits for post-selected metrology

Abstract:For unitary transformations, the quantum Fisher information (QFI) of a pure state is given by the uncertainty of the generator in that state. In post-selected metrology, the QFI is given by a modified expression describing conditional quantum statistics of the generator. Here, we show that the conditional generator uncertainties defined by post-selected QFI correspond to Ozawa-Hall uncertainties known from the theoretical analysis of quantum measurements. The post-selected measurement outcome updates the generator uncertainty according to the quantum statistics of that outcome. Enhancements of QFI beyond the maximal uncertainties of the generator eigenvalues are possible because post-selection tends to concentrate the largest part of the initial generator uncertainty in low probability outcomes of the post-selection measurement. Anomalous conditional uncertainties thus explain the extreme sensitivities that can be achieved in post-selected metrology.

arXiv:2608.26781 [quant-ph]

(or arXiv:2608.26781v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2608.26781 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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