2020
DOI: 10.1103/physrevlett.124.030501
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π -Corrected Heisenberg Limit

Abstract: We show that for the most general adaptive noiseless estimation protocol, where Uϕ = e iϕΛ is a unitary map describing the elementary evolution of the probe system, the asymptotically saturable bound on the precision of estimating ϕ takes the form ∆ϕ ≥ π n(λ + −λ − ) , where n is the number of applications of Uϕ, while λ+, λ− are the extreme eigenvalues of the generator Λ. This differs by a factor of π from the conventional bound, which is derived directly from the properties of the quantum Fisher information.… Show more

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Cited by 68 publications
(43 citation statements)
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“…Finally, we note that in this paper we have followed the frequentist estimation approach, and in principle more stringent HS bounds might be derived when following the Bayesian approach as was demonstrated recently in the single parameter case [75].…”
Section: Discussionmentioning
confidence: 91%
“…Finally, we note that in this paper we have followed the frequentist estimation approach, and in principle more stringent HS bounds might be derived when following the Bayesian approach as was demonstrated recently in the single parameter case [75].…”
Section: Discussionmentioning
confidence: 91%
“…Observe that the sample-mean estimator based on the rectangular window exhibits an O(1/ √ N ) scaling, while the others exhibit O(1/N ) scaling. This is a phenomenon that has also been observed in [18], which suggests that the rectangular window does not provide a substantial quantum speedup in the sense of RMSE scaling, since the O(1/N ) scaling (i.e., the "Heisenberg limit [25]) is an important characteristic of quantum algorithms conceived for phase estimation.…”
Section: Numerical Resultsmentioning
confidence: 77%
“…Even this finite improvement can be hard to achieve with better-than-Heisenberg strategies requiring either a very large number of repetitions [20,56] or a very large amount of prior knowledge [21,45]. Moreover, there is an extensive body of evidence supporting that a Heisenberg-scaling in the total number used across all repetitions cannot be surpassed [20,22,26,57,58].…”
Section: Discussionmentioning
confidence: 99%