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Evaluating the Holevo Cramér-Rao bound for multiparameter quantum metrology

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Albarelli, Francesco, Friel, Jamie F. and Datta, Animesh (2019) Evaluating the Holevo Cramér-Rao bound for multiparameter quantum metrology. Physical Review Letters, 123 (20). 200503. doi:10.1103/PhysRevLett.123.200503 ISSN 0031-9007.

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Official URL: http://dx.doi.org/10.1103/PhysRevLett.123.200503

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Abstract

Only with the simultaneous estimation of multiple parameters are the quantum aspects of metrology fully revealed. This is due to the incompatibility of observables. The fundamental bound for multiparameter quantum estimation is the Holevo Cram´er-Rao bound (HCRB) whose evaluation has so far remained elusive. For finite-dimensional systems we recast its evaluation as a semidefinite program, with reduced size for rank-deficient states. We show that it also satisfies strong duality. We use this result to study phase and loss estimation in optical interferometry and three-dimensional magnetometry with noisy multiqubit systems. For the former, we show that, in some regimes, it is possible to attain the HCRB with the optimal (single-copy) measurement for phase estimation. For the latter, we show a nontrivial interplay between the HCRB and incompatibility and provide numerical evidence that projective single-copy measurements attain the HCRB in the noiseless 2-qubit case.

Item Type: Journal Article
Subjects: Q Science > QC Physics
Divisions: Faculty of Science, Engineering and Medicine > Science > Physics
Library of Congress Subject Headings (LCSH): Physical measurements, Quantum theory, Quantum entanglement , Interferometry
Journal or Publication Title: Physical Review Letters
Publisher: American Physical Society
ISSN: 0031-9007
Official Date: 15 November 2019
Dates:
DateEvent
15 November 2019Published
27 September 2019Accepted
Volume: 123
Number: 20
Article Number: 200503
DOI: 10.1103/PhysRevLett.123.200503
Status: Peer Reviewed
Publication Status: Published
Reuse Statement (publisher, data, author rights): © 2019 American Physical Society
Access rights to Published version: Restricted or Subscription Access
Copyright Holders: 2019 American Physical Society
Date of first compliant deposit: 20 February 2020
Date of first compliant Open Access: 26 February 2020
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
EP/K04057X/2[EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266
EP/M01326X/1[EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266
EP/M013243/1[EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266
EP/L015315/1[EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266
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