Quantum advantage in postselected metrology

In every parameter-estimation experiment, the final measurement or the postprocessing incurs a cost. Postselection can improve the rate of Fisher information (the average information learned about an unknown parameter from a trial) to cost. We show that this improvement stems from the negativity of...

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Bibliographic Details
Published in:Nature communications 2020-07, Vol.11 (1), p.3775-3775, Article 3775
Main Authors: Arvidsson-Shukur, David R. M., Yunger Halpern, Nicole, Lepage, Hugo V., Lasek, Aleksander A., Barnes, Crispin H. W., Lloyd, Seth
Format: Article
Language:English
Subjects:
639/766/483/1139
639/766/483/1255
639/766/483/481
Commuting
Experiments
Fisher information
Humanities and Social Sciences
Mathematical analysis
Metrology
multidisciplinary
Parameter estimation
Probability distribution
Science
Science (multidisciplinary)
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Summary:In every parameter-estimation experiment, the final measurement or the postprocessing incurs a cost. Postselection can improve the rate of Fisher information (the average information learned about an unknown parameter from a trial) to cost. We show that this improvement stems from the negativity of a particular quasiprobability distribution, a quantum extension of a probability distribution. In a classical theory, in which all observables commute, our quasiprobability distribution is real and nonnegative. In a quantum-mechanically noncommuting theory, nonclassicality manifests in negative or nonreal quasiprobabilities. Negative quasiprobabilities enable postselected experiments to outperform optimal postselection-free experiments: postselected quantum experiments can yield anomalously large information-cost rates. This advantage, we prove, is unrealizable in any classically commuting theory. Finally, we construct a preparation-and-postselection procedure that yields an arbitrarily large Fisher information. Our results establish the nonclassicality of a metrological advantage, leveraging our quasiprobability distribution as a mathematical tool. In quantum metrology (as well as computing) it is not easy to pinpoint the specific source of quantum advantage. Here, the authors reveal a link between postselection and the unusually high rates of information per final measurement in general quantum parameter-estimation scenarios.
ISSN:2041-1723
2041-1723
DOI:10.1038/s41467-020-17559-w