Journal
NATURE COMMUNICATIONS
Volume 11, Issue 1, Pages -Publisher
NATURE PUBLISHING GROUP
DOI: 10.1038/s41467-020-17559-w
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Funding
- EPSRC
- Sweden-America Foundation
- Hitachi Ltd
- Lars Hierta's Memorial Foundation
- Girton College
- NSF
- Smithsonian Astrophysical Observatory
- European Union [642688]
- AFOSR
- ARO under the Blue Sky Initiative
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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.
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