All papers · LCP000050

Faithful and secure distributed quantum sensing under general-coherent attacks

Gabriele Bizzarri, Marco Barbieri, Mylenne Manrique, Miranda Parisi, Fabio Bruni, Ilaria Gianani, Matteo Rosati

npj Quantum Inf. 12, 33 (2026) · DOI: 10.1038/s41534-025-01180-0 · arXiv: 2505.02620

License: CC BY 4.0.

Abstract

Quantum metrology and cryptography can be combined in a distributed and/or remote sensing setting, where distant end-users with limited quantum capabilities can employ quantum states, transmitted by a quantum-powerful provider via a quantum network, to perform quantum-enhanced parameter estimation in a private fashion. Previous works on the subject have been limited by restricted assumptions on the capabilities of a potential eavesdropper and the use of abort-based protocols that prevent a simple practical realization. Here we introduce, theoretically analyze, and experimentally demonstrate single- and two-way protocols for distributed sensing combining several unique and desirable features: (i) a safety-threshold mechanism that allows the protocol to proceed in low-noise cases and quantifying the potential tampering with respect to the ideal estimation procedure, effectively paving the way for wide-spread practical realizations; (ii) equivalence of entanglement-based and mutually-unbiased-bases-based formulations; (iii) robustness against collective attacks via a LOCC-de-Finetti theorem, for the first time to our knowledge. Finally, we demonstrate our protocols in a photonic-based implementation, observing that the possibility of guaranteeing a safety threshold may come at a significant price in terms of the estimation bias, potentially overestimating the effect of tampering in practical settings.

Figures

8 panels with data across 4 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.

Fig. 2

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

Fig. 3

• panel (1): Top panel: retrieved phase estimate $E\hat{\phi}^{\prime}$ against plate setting $\theta$ (degrees). Blue points are the experimental estimates; the red line is the ideal expectation $\phi^{\prime}=2\theta$. data.csv
• panel (2): Bottom panel: experimental phase-estimate variance $\Delta^2\hat{\phi}^{\prime}$ against plate setting $\theta$ (degrees), shown as blue points. The horizontal red line is the ideal Cramér-Rao bound. data.csv

Fig. 4

• panel (1): Top panel: magnitude of experimental phase-estimation bias relative to the ideal case against plate setting $\theta$ (degrees), on a logarithmic vertical axis. Blue points are observations; the red curve is the fidelity-based bound (6). data.csv
• panel (2): Bottom panel: magnitude of the experimental variance discrepancy from the ideal case against plate setting $\theta$ (degrees), on a logarithmic vertical axis. Blue points are observations; the red curve is bound (7). data.csv

Fig. 5

• panel (1): Bound (6) on the bias with respect to the ideal case, $|\mathbb{E}\hat{\phi}^{\prime}-\mathbb{E}\hat{\phi}|$, against $\phi$ ($^\circ$), for a dephasing channel with $p = 0.9$ and $N = 1000$ (top panel). Only the red bound is shown; the printed blue bias curve is not. data.csv
• panel (2): Bound (7) on the variance discrepancy, $|\Delta^2\hat{\phi}^{\prime}-\Delta^2\hat{\phi}|$, against $\phi$ ($^\circ$), for the same dephasing channel (bottom panel). Only the red bound is shown; the printed blue discrepancy curve is not. data.csv

Fig. 6

• panel (1): Bound (6) on the bias with respect to the ideal case, $|\mathbb{E}\hat{\phi}^{\prime}-\mathbb{E}\hat{\phi}|$, against $\phi$ ($^\circ$), for a depolarising channel with $p = 0.93$ and $N = 1000$ (top panel), evaluated with $\epsilon_0 = \epsilon$ as the printed curve is. Only the red bound is shown; the printed blue bias curve is not. data.csv
• panel (2): Bound (7) on the variance discrepancy, $|\Delta^2\hat{\phi}^{\prime}-\Delta^2\hat{\phi}|$, against $\phi$ ($^\circ$), for the same depolarising channel (bottom panel), evaluated with $\epsilon_0 = \epsilon$ as the printed curve is. The discrepancy itself is identically zero for this channel, so the bound is the only curve in the printed panel. data.csv

Cite

Gabriele Bizzarri, Marco Barbieri, Mylenne Manrique, Miranda Parisi, Fabio Bruni, Ilaria Gianani, Matteo Rosati. Faithful and secure distributed quantum sensing under general-coherent attacks. npj Quantum Inf. 12, 33 (2026). https://doi.org/10.1038/s41534-025-01180-0

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