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Quantum advantage in postselected metrology

Published version
Peer-reviewed

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Authors

Arvidsson-Shukur, David R. M.  ORCID logo  https://orcid.org/0000-0002-0185-0352
Yunger Halpern, Nicole  ORCID logo  https://orcid.org/0000-0001-8670-6212
Lasek, Aleksander A.  ORCID logo  https://orcid.org/0000-0001-8077-8178
Barnes, Crispin H. W. 

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.

Description

Keywords

Article, /639/766/483/481, /639/766/483/1139, /639/766/483/1255, article

Journal Title

Nature Communications

Conference Name

Journal ISSN

2041-1723

Volume Title

11

Publisher

Nature Publishing Group UK
Sponsorship
RCUK | Engineering and Physical Sciences Research Council (EPSRC) (RG 90769)