Composable privacy of networked quantum sensing

TL;DR

This work tackles the privacy of distributed quantum sensing by placing networked parameter estimation in the framework of abstract cryptography to achieve universally composable security. It proves that two existing quasi-privacy definitions are composably secure (with explicit bounds) and demonstrates full composable privacy for a GHZ-based mean-estimation task; it then extends to general functions and analyzes the role of the quantum Fisher information in privacy proofs. By linking QFI-based privacy notions with constructive cryptography, it enables rigorous secure-composition of privacy-preserving metrology protocols and shows how state verification can be integrated via modular resources. The results pave the way for securely embedding quantum-enhanced networked sensing protocols in larger cryptographic or metrological pipelines, with clear guidance on when privacy degrades under compositional use. Key takeaways include explicit $\,\\varepsilon$-bounds tied to privacy measures $\\mathcal{P}$ and $\\mathcal{Q}$, and a principled path to verify and compose private quantum sensing in realistic networks.

Abstract

Networks of sensors are a promising scheme to deliver the benefits of quantum technologies in coming years, offering enhanced precision and accuracy for distributed metrology through the use of large entangled states. Recent work has additionally explored the privacy of these schemes, meaning that local parameters can be kept secret while a joint function of these is estimated by the network. In this work, we use the abstract cryptography framework to relate the two proposed definitions of quasi-privacy, showing that both are composable, which enables the protocol to be securely included as a sub-routine to other schemes. We give an explicit example that estimating the mean of a set of parameters using GHZ states is composably fully secure.

Figures (5)

• Figure 1: One round of the quantum parameter estimation protocol, adapted from dejong2025anonymous. A state $\rho$ is distributed across the network, then the parameters are encoded through the channels $\Lambda_\mu (\theta_\mu)$. Each party measures its own part of the state, and return the measurements to the rest of the network. The output at each round is collected and used to estimate $f(\boldsymbol{\theta})$.
• Figure 2: The interactions between systems in a constructive cryptographic proof. Given a concrete resource $\mathcal{R}$ and an ideal resource $\mathcal{S}$, a distinguisher $\sigma$ is constructed so that a distinguisher $\mathcal{D}$ cannot distinguish between $\sigma \mathcal{S}$ and $\mathcal{R}$. Roughly, this means that $\mathcal{R}$ is not revealing any information that is not already revealed by $\mathcal{S}$.
• Figure 3: A representation of the ideal resource $\mathcal{S}$, with (a) and without (b) the filter $\Diamond$ applied, for $n$ parties, with left interfaces used for honest parties and interfaces below the resource for dishonest interfaces (the label is omitted on the right hand figure).
• Figure 4: $\pi_H \mathcal{R}$: A representation of the concrete resource $\mathcal{R}$, where the converter $\pi_H$ corresponding to honest behaviour is applied only to the honest interfaces, $H$. We only show $N=1$, and the details of $\pi_H$ are in Alg. \ref{['honest protocol']}. The label $q_\mu$ corresponds to a qubit, whereas $o_\mu$ are measurement outcomes.
• Figure 5: $\sigma_H \mathcal{S} \sigma_D$: A representation of the ideal resource $\mathcal{S}$, where the simulators $\sigma_H$ and $\sigma_D$ are applied to the corresponding interfaces. We only show $N=1$. For the security proof, this is compared to Fig. \ref{['fig: concrete resource']}. We also omit the communication between simulators, which can be done through using $\mathcal{S}$, thus we only show the basic functionality of the simulators in reproducing the quantum state and measurement statistics.

Theorems & Definitions (11)

• Definition 1
• Theorem 2
• proof
• Lemma 3
• proof
• Definition 4: Bugalho et al., bugalho2025private
• Theorem 5
• proof
• Definition 6: Hassani et al., hassani2025privacy
• Theorem 7