Anonymous and private parameter estimation in networks of quantum sensors

TL;DR

The paper presents APPE, the first protocol for anonymous private parameter estimation in quantum sensor networks. It leverages GHZ entanglement and a combination of NOTIFICATION, VOTE, and state verification to privately estimate the mean of a selected subset's local parameters while concealing both parameter values and participant identities. The authors provide rigorous guarantees for integrity, privacy, and anonymity, including explicit bias bounds and a privacy formalism based on quantum Fisher information. They also discuss practical limitations, notably the reliance on high-fidelity GHZ states and memory, and outline directions to make the approach scalable and robust in real-world quantum networks.

Abstract

Anonymity and privacy are two key properties of modern communication networks. In quantum networks, distributed quantum sensing has emerged as a powerful use case, with applications to clock synchronisation, detecting gravitational effects and more. In this work, we develop a new protocol that, for the first time, combines the different cryptographic properties of anonymity and privacy for the task of distributed parameter estimation. That is, we present a protocol that allows a selected subset of network participants to anonymously collaborate in estimating the average of their private parameters. Crucially, this is achieved without disclosing either the individual parameter values or the identities of the participants, neither to each other nor to the broader network.

Figures (2)

• Figure 1: Illustration of ANONYMOUS PRIVATE PARAMETER ESTIMATION on an example of a network of $n=6$ agents, where $a_{3}$ is the co-ordinator Alice, $\mathcal{A}$, and starts the protocol. In the first step, the nodes run NOTIFICATION to allow Alice to anonymously notify the set of $m=4$ participants $\{a_{2}, a_{3}, a_{4}, a_{6}\}$. In the second step the agents run VOTE for the participants to verify $m$. During this round, participants vote anonymously $v_{2}=v_{3}=v_{4}=v_{6}=1$, and, in an honest scenario, non-participants vote $v_{1}=v_{5}=0$. Next the network runs STATE VERIFICATION to ensure that all agents share a state sufficiently close to a $\mathrm{GHZ}$ state. Using a secret key Alice can then communicate to the participants whether the state is used for PARITY VERIFICATION (PV) or PARITY ESTIMATION (PE). In PV, everyone measures their qubit in the $X$-basis and it is used as trap round to verify that non-participants do not tamper with the desired estimation. In PE, the participants first apply a rotation on their qubit using their private parameter and then measure in the $X$-basis, while non-participants are expected to just measure. By repeating PE enough times, Alice can estimate $\bar{\theta}_\mathcal{P}$.
• Figure 2: Illustrative example of the selection and use of target states $\tilde{\rho}$ from each round. In this example, five of the total $L$ rounds are shown. In each round a certain number of states are measured and tested to be $\mathrm{GHZ}$ states. Of the remaining states one is chosen to be the target state$\tilde{\rho}$ highlighted in grey in the figure. The target state is then used for PE or PV, according to the key $\kappa$ generated during ACKA.

Theorems & Definitions (5)

• Remark
• Lemma 1
• Definition 1
• Definition 2
• Definition 3