Quantum advantage in postselected metrology

David R. M. Arvidsson-Shukur (), Nicole Yunger Halpern, Hugo V. Lepage, Aleksander A. Lasek, Crispin H. W. Barnes and Seth Lloyd
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David R. M. Arvidsson-Shukur: University of Cambridge
Nicole Yunger Halpern: Massachusetts Institute of Technology
Hugo V. Lepage: University of Cambridge
Aleksander A. Lasek: University of Cambridge
Crispin H. W. Barnes: University of Cambridge
Seth Lloyd: Massachusetts Institute of Technology

Nature Communications, 2020, vol. 11, issue 1, 1-7

Abstract: Abstract 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.

Date: 2020
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DOI: 10.1038/s41467-020-17559-w

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