Minimax Quantum Tomography: Estimators and Relative Entropy Bounds

Ferrie, C; Blume-Kohout, R

Minimax Quantum Tomography: Estimators and Relative Entropy Bounds

Ferrie, C

Blume-Kohout, R

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Publication Type:: Journal Article
Citation:: Physical Review Letters, 2016, 116 (9)
Issue Date:: 2016-03-04

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Field	Value	Language
dc.contributor.author	Ferrie, C https://orcid.org/0000-0003-2736-9943	en_US
dc.contributor.author	Blume-Kohout, R	en_US
dc.date.issued	2016-03-04	en_US
dc.identifier.citation	Physical Review Letters, 2016, 116 (9)	en_US
dc.identifier.issn	0031-9007	en_US
dc.identifier.uri	http://hdl.handle.net/10453/106707
dc.description.abstract	© 2016 American Physical Society. A minimax estimator has the minimum possible error ("risk") in the worst case. We construct the first minimax estimators for quantum state tomography with relative entropy risk. The minimax risk of nonadaptive tomography scales as O(1/N) - in contrast to that of classical probability estimation, which is O(1/N) - where N is the number of copies of the quantum state used. We trace this deficiency to sampling mismatch: future observations that determine risk may come from a different sample space than the past data that determine the estimate. This makes minimax estimators very biased, and we propose a computationally tractable alternative with similar behavior in the worst case, but superior accuracy on most states.	en_US
dc.relation.ispartof	Physical Review Letters	en_US
dc.relation.isbasedon	10.1103/PhysRevLett.116.090407	en_US
dc.subject.classification	General Physics	en_US
dc.title	Minimax Quantum Tomography: Estimators and Relative Entropy Bounds	en_US
dc.type	Journal Article
utslib.citation.volume	9	en_US
utslib.citation.volume	116	en_US
utslib.for	0206 Quantum 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	9	en_US
pubs.publication-status	Published	en_US
pubs.volume	116	en_US

Abstract:

© 2016 American Physical Society. A minimax estimator has the minimum possible error ("risk") in the worst case. We construct the first minimax estimators for quantum state tomography with relative entropy risk. The minimax risk of nonadaptive tomography scales as O(1/N) - in contrast to that of classical probability estimation, which is O(1/N) - where N is the number of copies of the quantum state used. We trace this deficiency to sampling mismatch: future observations that determine risk may come from a different sample space than the past data that determine the estimate. This makes minimax estimators very biased, and we propose a computationally tractable alternative with similar behavior in the worst case, but superior accuracy on most states.

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http://hdl.handle.net/10453/106707