Parameter estimation with limited access of measurements

Quantum 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 work, we present a theoretical framework to explore the parameter estimation with limited access of measurements by analyzing the effect of non-optimal measurement on the estimation precision. We define a quantity $\Lambda$ to characterize the effect and illustrate how to optimize observables to attain a bound with limited accessibility of observables. On the other side, we define a Euclidean distance to quantify the difference between an observable and the optimal ones in terms of 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 non-optimal measurement on the estimation of the transition frequency for a driven quantum bit. While in the second example, we consider a bipartite system, in which one of them is measurement inaccessible. To be specific, we take the NV-center in diamond as the bipartite system, where the NV-center electronic spin interacts with a single nucleus via the dipole-dipole interactions. We achieve a precise estimation for the nuclear Larmor frequency by optimizing only the observables of the electron. We find that the observable closed to the optimal ones better the estimation precision. This provides us with a criterion to find a measurement for parameter estimation in case the optimal ones are inaccessible.Comment: 11 pages, 4 figure

The Quadratic Shortest Path Problem and its Genetic Algorithm

The quadratic shortest path (QSP) problem is to find a path from a node to another node in a given network such that the total cost includes two kinds of costs, say direct cost and interactive cost, is minimum. The direct cost is the cost associated with each arc and the interactive cost occurs when two arcs appear simultaneously in the shortest path. In this paper, the concept of the quadratic shortest path is initialized firstly. Then a spanning tree-based genetic algorithm is designed for solving the quadratic shortest path problem. Finally, a numerical example is given

The influence of passivation and photovoltaic properties of α-Si:H coverage on silicon nanowire array solar cells

Silicon nanowire (SiNW) arrays for radial p-n junction solar cells offer potential advantages of light trapping effects and quick charge collection. Nevertheless, lower open circuit voltages (V(oc)) lead to lower energy conversion efficiencies. In such cases, the performance of the solar cells depends critically on the quality of the SiNW interfaces. In this study, SiNW core-shell solar cells have been fabricated by growing crystalline silicon (c-Si) nanowires via the metal-assisted chemical etching method and by depositing hydrogenated amorphous silicon (α-Si:H) via the plasma-enhanced chemical vapor deposition (PECVD) method. The influence of deposition parameters on the coverage and, consequently, the passivation and photovoltaic properties of α-Si:H layers on SiNW solar cells have been analyzed