Parameter estimation with limited access to measurements
At a Glance
Section titled āAt a Glanceā| Metadata | Details |
|---|---|
| Publication Date | 2024-03-18 |
| Journal | Physical review. A/Physical review, A |
| Authors | Jianning Li, Dianzhen Cui, X. X. Yi |
| Institutions | Northeast Normal University |
Abstract
Section titled āAbstractāQuantum parameter estimation holds the promise of quantum technologies, in which physical parameters can be measured with much greater precision than what is achieved with classical technologies. However, how to obtain the best precision when the optimal measurement is not accessible is still an open problem. In this paper, we present a theoretical framework to explore the parameter estimation with limited access of measurements by analyzing the effect of nonoptimal measurement on the estimation precision. We define a quantity $\mathrm{\ensuremath{\Lambda}}$ to characterize the effect and illustrate how to optimize observables to attain a bound with limited accessibility of observables. In addition, we introduce the minimum Euclidean distance to quantify the difference between an observable and the optimal ones in terms of the Frobenius norm and find that the measurement with a shorter distance to the optimal ones benefits the estimation. Two examples are presented to show our theory. In the first, we analyze the effect of nonoptimal measurement on the estimation precision of the transition frequency for a driven qubit. In the second example, we consider a bipartite system, in which one of them is measurement inaccessible. To be specific, we take a toy model, the nitrogen-vacancy (NV) center in diamond, as the bipartite system, where the NV-center electronic spin interacts with a single nucleus via the dipole-dipole interaction. We achieve a precise estimation for the nuclear Larmor frequency by optimizing only the observables of the electronic spin. In these two examples, the minimum Euclidean distance between an observable and the optimal ones is analyzed and the results show that the closer the observable to the optimal ones the better the estimation precision. This paper establishes a relation between the estimation precision and the distance of the nonoptimal observable to the optimal ones, which could be helpful for experiments seeking the best observable in parameter estimation.
Tech Support
Section titled āTech SupportāOriginal Source
Section titled āOriginal SourceāReferences
Section titled āReferencesā- 1976 - Quantum Detection and Estimation Theory
- 1982 - Probabilistic and Statistical Aspects of Quantum Theory
- 1946 - Mathematical Methods of Statistics