Weak value amplification is suboptimal for estimation and detection

Ferrie, C; Combes, J

Weak value amplification is suboptimal for estimation and detection

Ferrie, C

Combes, J

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Publication Type:: Journal Article
Citation:: Physical Review Letters, 2014, 112 (4)
Issue Date:: 2014-01-31

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Field	Value	Language
dc.contributor.author	Ferrie, C https://orcid.org/0000-0003-2736-9943	en_US
dc.contributor.author	Combes, J	en_US
dc.date.issued	2014-01-31	en_US
dc.identifier.citation	Physical Review Letters, 2014, 112 (4)	en_US
dc.identifier.issn	0031-9007	en_US
dc.identifier.uri	http://hdl.handle.net/10453/118942
dc.description.abstract	We show by using statistically rigorous arguments that the technique of weak value amplification does not perform better than standard statistical techniques for the tasks of single parameter estimation and signal detection. Specifically, we prove that postselection, a necessary ingredient for weak value amplification, decreases estimation accuracy and, moreover, arranging for anomalously large weak values is a suboptimal strategy. In doing so, we explicitly provide the optimal estimator, which in turn allows us to identify the optimal experimental arrangement to be the one in which all outcomes have equal weak values (all as small as possible) and the initial state of the meter is the maximal eigenvalue of the square of the system observable. Finally, we give precise quantitative conditions for when weak measurement (measurements without postselection or anomalously large weak values) can mitigate the effect of uncharacterized technical noise in estimation. © 2014 American Physical Society.	en_US
dc.relation.ispartof	Physical Review Letters	en_US
dc.relation.isbasedon	10.1103/PhysRevLett.112.040406	en_US
dc.subject.classification	General Physics	en_US
dc.title	Weak value amplification is suboptimal for estimation and detection	en_US
dc.type	Journal Article
utslib.citation.volume	4	en_US
utslib.citation.volume	112	en_US
utslib.for	0206 Quantum Physics	en_US
utslib.for	0105 Mathematical Physics	en_US
utslib.for	01 Mathematical Sciences	en_US
utslib.for	02 Physical Sciences	en_US
utslib.for	09 Engineering	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Strength - QSI - Centre for Quantum Software and Information
utslib.copyright.status	open_access
pubs.issue	4	en_US
pubs.publication-status	Published	en_US
pubs.volume	112	en_US

Abstract:

We show by using statistically rigorous arguments that the technique of weak value amplification does not perform better than standard statistical techniques for the tasks of single parameter estimation and signal detection. Specifically, we prove that postselection, a necessary ingredient for weak value amplification, decreases estimation accuracy and, moreover, arranging for anomalously large weak values is a suboptimal strategy. In doing so, we explicitly provide the optimal estimator, which in turn allows us to identify the optimal experimental arrangement to be the one in which all outcomes have equal weak values (all as small as possible) and the initial state of the meter is the maximal eigenvalue of the square of the system observable. Finally, we give precise quantitative conditions for when weak measurement (measurements without postselection or anomalously large weak values) can mitigate the effect of uncharacterized technical noise in estimation. © 2014 American Physical Society.

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http://hdl.handle.net/10453/118942