Evaluating the Holevo Cramér-Rao Bound for Multiparameter Quantum Metrology

Francesco Albarelli, Jamie F. Friel, and Animesh Datta
Phys. Rev. Lett. 123, 200503 – Published 15 November 2019
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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 Cramér-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.

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  • Received 13 June 2019
  • Revised 26 August 2019

DOI:https://doi.org/10.1103/PhysRevLett.123.200503

© 2019 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & TechnologyAtomic, Molecular & Optical

Authors & Affiliations

Francesco Albarelli1,*, Jamie F. Friel1,2,†, and Animesh Datta1,‡

  • 1Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
  • 2EPSRC Centre for Doctoral Training in Diamond Science and Technology, University of Warwick, Coventry CV4 7AL, United Kingdom

  • *francesco.albarelli@gmail.com
  • j.friel@warwick.ac.uk
  • animesh.datta@warwick.ac.uk

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Issue

Vol. 123, Iss. 20 — 15 November 2019

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