Quantum steering, a type of quantum correlation with unique asymmetry, has important applications in asymmetric quantum information tasks. We consider a new quantum steering scenario in which one half of a two-qubit Werner state is sequentially measured by multiple Alices and the other half by multiple Bobs. We find that the maximum number of Alices who can share steering with a single Bob increases from 2 to 5 when the number of measurement settings N increases from 2 to 16. Furthermore, we find a counterintuitive phenomenon that for a fixed N, at most 2 Alices can share steering with 2 Bobs, while 4 or more Alices are allowed to share steering with a single Bob. We further analyze the robustness of the steering sharing by calculating the required purity of the initial Werner state, the lower bound of which varies from 0.503(1) to 0.979(5). Finally, we show that our both-sides sequential steering sharing scheme can be applied to control the steering ability, even the steering direction, if an initial asymmetric state or asymmetric measurement is adopted. Our work gives insights into the diversity of steering sharing and can be extended to study the problems such as genuine multipartite quantum steering when the sequential unsharp measurement is applied.

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We develop a method to quantify the superposition state of two different Laguerre–Gaussian modes. By analyzing the characteristics of the intensity distribution obtained in a single measurement, including the petal number, the position and value of the extremum intensity, one can quantify the angular momentum index, the radial node index and the superposition coefficient simultaneously. Experimentally, we measure a series of superposition states, whose angular momentum index ranges from −47 to 53, radial node index from 0 to 3 and superposition weight from 0.1 to 0.9. The average trace distance and the mean fidelity of these states are lower than 0.053 ± 0.001 and higher than 0.982 ± 0.002, respectively. Our method can further obtain the superposition coefficient compared with previous mode verification ones and can reduce the number of measurement settings compared with the traditional quantum state tomography, thus more applicable in practice.

High-precision surface roughness estimation plays an important role in many applications. However, the classical estimating methods are limited by shot noise and only can achieve the precision of 0.1 nm with white light interferometer. Here, we propose two weak measurement schemes to estimate surface roughness through spectrum analysis and intensity analysis. The estimating precision with spectrum analysis is about 10 −5 nm by using a currently available spectrometer with the resolution of ∆λ = 0.04 pm and the corresponding sensitivity is better than 0.1 THz/nm. And the precision and sensitivity of the light intensity analysis scheme achieve as high as 0.07 nm and 1/nm, respectively. By introducing a modulated phase, we show that the sensitivity and precision achieved in our schemes can be effectively retained in a wider dynamic range. We further provide the experimental design of the surface profiler based on our schemes. It simultaneously meets the requirements of high precision, high sensitivity, and wide measurement range, making it to be a promising practical tool.