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  • Open Access

Privacy in Continuous-Variable Distributed Quantum Sensing

A. de Oliveira Junior1,*, Anton L. Andersen2, Benjamin Lundgren Larsen1, Sean William Moore2, Damian Markham2, Masahiro Takeoka3,4, Jonatan Bohr Brask1, and Ulrik L. Andersen1

  • *Contact author: alexssandredeoliveira@gmail.com
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PRX Quantum 7, 033036 – Published 21 August, 2026

DOI: https://doi.org/10.1103/1zsz-clqx

Abstract

Can a distributed network of quantum sensors estimate a global parameter while protecting every locally encoded value? We answer this question affirmatively by introducing and analyzing a protocol for distributed quantum sensing in the continuous-variable regime. We consider a multipartite network in which an unknown local phase is imprinted at each node on a shared entangled Gaussian state. We show that the average phase can be estimated with high precision, exhibiting Heisenberg scaling in the total photon number, while individual phases are inaccessible. We further prove a no-go theorem showing that, for three or more parties, no finite-energy Gaussian probe can provide complete privacy of the average phase, meaning that all phase combinations orthogonal to the average remain entirely hidden. This identifies the two-party case as an exceptional Gaussian setting that can achieve complete privacy. We further investigate the impact of displacements and optical losses, revealing trade-offs between estimation accuracy and privacy. Finally, we benchmark the protocol against other continuous-variable resource states.

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Popular Summary

When speaking of quantum technologies, quantum networks—where distant parties share an entangled state to accomplish tasks beyond classical capabilities—stand out as a defining feature. Each party, potentially far apart in space, accesses its share of the state and encodes information onto it, which is later used collectively for tasks such as sensing, communication, or computing. Despite our growing understanding of quantum networks, a central question remains: how can we ensure that the information encoded by each party stays private and secure?

We approached this problem by considering a sensing task in which each sensor measures and encodes a local value, while the network is authorized to reveal only the average of all these values. The individual reading from any one sensor should remain hidden. Our framework determines which combinations of the locally encoded values can be learned from the network and which remain inaccessible. Unexpectedly, we found a fundamental limitation: with three or more sensors, finite-energy Gaussian states cannot reveal only the average while hiding every other combination of values. Nevertheless, we designed a practical optical protocol that protects each individual reading. The average can be estimated with a precision that improves at the strongest rate allowed by quantum mechanics as more light is used, while no individual contribution can be uniquely recovered.

Our work clarifies the balance between precision and privacy in continuous-variable quantum networks and shows how realistic imperfections affect it. Because the protocol relies only on established optical components, including squeezed-light sources, beam splitters, and homodyne detectors, it offers a realistic route toward privacy-preserving quantum sensor networks.

Article Text

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PRX Quantum 7, 033036– Published 21 August, 2026
  • Received 25 September 2025
  • Accepted 27 July 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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