Quantum advantage in postselected metrology

• Published in: Nature communications Vol. 11; no. 1; p. 3775
• Main Authors: Arvidsson-Shukur, David R M, Yunger Halpern, Nicole, Lepage, Hugo V, Lasek, Aleksander A, Barnes, Crispin H W, Lloyd, Seth
• Format: Journal Article
• Language: English
• Published: England Nature Publishing Group 29.07.2020; Nature Publishing Group UK; Nature Portfolio
• Subjects: Commuting; Experiments; Fisher information; Mathematical analysis; Metrology; Parameter estimation; Probability distribution
• 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.