Quantum advantage in postselected metrology

• 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)
• ISSN: 2041-1723; 2041-1723
• DOI: 10.1038/s41467-020-17559-w

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.