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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
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Official URL: http://dx.doi.org/10.1103/PhysRevLett.123.200503
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 | |||||||||||||||
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| Subjects: | Q Science > QC Physics | |||||||||||||||
| Divisions: | Faculty of 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: |
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| Date of first compliant deposit: | 20 February 2020 | |||||||||||||||
| Date of first compliant Open Access: | 26 February 2020 | |||||||||||||||
| Volume: | 123 | |||||||||||||||
| Number: | 20 | |||||||||||||||
| Article Number: | 200503 | |||||||||||||||
| DOI: | 10.1103/PhysRevLett.123.200503 | |||||||||||||||
| Status: | Peer Reviewed | |||||||||||||||
| Publication Status: | Published | |||||||||||||||
| Publisher Statement: | © 2019 American Physical Society | |||||||||||||||
| Access rights to Published version: | Restricted or Subscription Access | |||||||||||||||
| Copyright Holders: | 2019 American Physical Society | |||||||||||||||
| RIOXX Funder/Project Grant: |
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