Distributed quantum sensing with measurement-after-interaction strategies

npj Quantum Inf. 12, 84 (2026) · DOI: 10.1038/s41534-026-01224-z

License: CC BY 4.0.

Abstract

We investigate multiparameter quantum estimation protocols based on measurement-after-interaction (MAI) strategies, in which the probe state undergoes an additional evolution prior to linear measurements. As we show in our study, this extra evolution enables different level of advantages depending on whether it is implemented locally or nonlocally across the sensing nodes. By benchmarking MAI strategies in both discrete- and continuous-variable systems, we show that they can significantly enhance multiparameter sensitivity and robustness against detection noise, particularly when non-Gaussian probe states are employed, cases where standard linear measurements are often insufficient. We also derive analytical results for multiparameter squeezing and establish the corresponding scaling laws for spin-squeezed states, demonstrating that MAI protocols can reach the Heisenberg scaling. These results can be implemented in state-of-the-art experimental platforms involving atomic ensembles or optical fields.

Figures

3 panels with data across 2 figures. Each panel page shows the plot, its columns and its files; each data.csv begins with a header naming the paper, the panel, the source, the license and the provenance route.

Fig. 1

Illustrative figure, no extractable data. Shown in the paper PDF. Page 2 of the PDF.

Fig. 2

• panel (b): Quantum gain (dB) against the evolution time $\mu = 2\chi t$ for $N = 100$: nonlocal MAI (red), local MAI for $M = 2$, 4, 10 and 20 (orange, fading with $M$) and linear measurements L (blue). The print draws the $M = 100$ local curve dashed on top of L; it is not a separate series here. data.csv
• panel (c): Quantum gain (dB) against total atom number $N$ (log axis) for linear measurements L (blue), nonlocal MAI (red) and local MAI with $M = 2$ (orange). The print's arrows and scaling labels $\xi^{-2}_{\mathrm{MAI},\alpha} \sim N$ and $\xi^{-2}_{\mathrm{L}} \sim N^{2/3}$ are not hosted. data.csv

Fig. 3

• panel (a): Quantum gain (dB) against the standard deviation $\sigma$ of Gaussian detection noise for a two-mode squeezed vacuum with $r = 0.5$: linear measurements L (blue), nonlocal MAI (red) and local MAI (orange dotted) with $r_{\mathrm{nl}} = r_{\mathrm{loc}} = r$; the two MAI curves coincide. data.csv

Cite

Jiajie Guo, Shuheng Liu, Matteo Fadel, Qiongyi He. Distributed quantum sensing with measurement-after-interaction strategies. npj Quantum Inf. 12, 84 (2026). https://doi.org/10.1038/s41534-026-01224-z

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