Robust guaranteed-cost adaptive quantum phase estimation

Shibdas Roy, Dominic W. Berry, Ian R. Petersen, Elanor H. Huntington

Research output: Contribution to journalArticleResearchpeer-review

Abstract

Quantum parameter estimation plays a key role in many fields like quantum computation, communication, and metrology. Optimal estimation allows one to achieve the most precise parameter estimates, but requires accurate knowledge of the model. Any inevitable uncertainty in the model parameters may heavily degrade the quality of the estimate. It is therefore desired to make the estimation process robust to such uncertainties. Robust estimation was previously studied for a varying phase, where the goal was to estimate the phase at some time in the past, using the measurement results from both before and after that time within a fixed time interval up to current time. Here, we consider a robust guaranteed-cost filter yielding robust estimates of a varying phase in real time, where the current phase is estimated using only past measurements. Our filter minimizes the largest (worst-case) variance in the allowable range of the uncertain model parameter(s) and this determines its guaranteed cost. It outperforms in the worst case the optimal Kalman filter designed for the model with no uncertainty, which corresponds to the center of the possible range of the uncertain parameter(s). Moreover, unlike the Kalman filter, our filter in the worst case always performs better than the best achievable variance for heterodyne measurements, which we consider as the tolerable threshold for our system. Furthermore, we consider effective quantum efficiency and effective noise power, and show that our filter provides the best results by these measures in the worst case.

LanguageEnglish
Article number052322
Pages1-16
Number of pages16
JournalPhysical Review A
Volume95
Issue number5
DOIs
Publication statusPublished - 11 May 2017

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costs
filters
Kalman filters
estimates
quantum computation
metrology
quantum efficiency
communication
intervals
thresholds

Bibliographical note

S. Roy, D. W. Berry, I. R. Petersen, and E. H. Huntington, Phys. Rev. A, 95, 052322, 2017. Copyright 2017 by the American Physical Society. The original article can be found at http://dx.doi.org./10.1103/PhysRevA.95.052322.

Cite this

Roy, Shibdas ; Berry, Dominic W. ; Petersen, Ian R. ; Huntington, Elanor H. / Robust guaranteed-cost adaptive quantum phase estimation. In: Physical Review A. 2017 ; Vol. 95, No. 5. pp. 1-16.
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Roy, S, Berry, DW, Petersen, IR & Huntington, EH 2017, 'Robust guaranteed-cost adaptive quantum phase estimation', Physical Review A, vol. 95, no. 5, 052322, pp. 1-16. https://doi.org/10.1103/PhysRevA.95.052322

Robust guaranteed-cost adaptive quantum phase estimation. / Roy, Shibdas; Berry, Dominic W.; Petersen, Ian R.; Huntington, Elanor H.

In: Physical Review A, Vol. 95, No. 5, 052322, 11.05.2017, p. 1-16.

Research output: Contribution to journalArticleResearchpeer-review

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