Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2509.12338

Privacy in continuous-variable distributed quantum sensing

Junior, A. de Oliveira, Andersen, Anton L., Benjamin Lindegren Larsen, Sean William Moore, Damian Markham, Masahiro Takeoka, Jonatan Bohr Brask, Ulrik L. Andersen

Published Sep 15, 2025• 0 citations
arXivHTMLPDF

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 analysing 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.

DOI
10.48550/arxiv.2509.12338

Related papers

Privacy in Continuous-Variable Distributed Quantum Sensing

A. de Oliveira, Anton L. Andersen, Benjamin Lindegren Larsen +5 more

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.

PRX Quantum•Jul 27, 2026•0 citations

Optimal Gaussian networks for private distributed quantum sensing

Hanbom Yoo, Byeongyun Yang, Hyunwoo Yoo +1 more

Private distributed quantum sensing aims to estimate an authorized collective parameter while preventing independent estimation of individual local parameters. Here, we analytically characterize Gaussian quantum networks satisfying this perfect local privacy condition. Using a graph representation of the Gaussian pairing matrix, we show that two-mode squeezed vacuum states constitute the essential building blocks of privacy-preserving Gaussian states. We then analytically derive the optimal sensitivity under perfect local privacy and determine a Gaussian probe that achieves Heisenberg scaling with respect to both the photon number and the number of sensing modes. Using local homodyne measurements and maximum-likelihood estimation, we numerically verify quantum-enhanced sensitivity beyond the shot-noise limit while preserving perfect local privacy. We further show that the local-privacy condition is preserved under arbitrary phase-independent quantum channels, including optical loss. Our results provide a general framework for constructing and optimizing privacy-preserving continuous-variable quantum sensing networks.

quant-pharXiv:2608.27136•Aug 28, 2026•0 citations

Privacy in distributed quantum sensing with Gaussian quantum networks

Uesli Alushi, Roberto Di Candia

We study the privacy properties of distributed quantum sensing protocols in a Gaussian quantum network, where each node encodes a parameter via a local phase shift. We first show that perfect privacy and optimal precision are jointly achievable using specifically tailored multimode photon-number correlated states. We then consider Gaussian states, which are experimentally less demanding as they can be implemented using only linear optics and two-photon parametric processes. Focusing on fully symmetric Gaussian states, we show that for networks with more than two nodes, perfect privacy can be achieved only asymptotically, in the limit of large photon numbers. However, we show that optimized fully-symmetric Gaussian states enable improved privacy levels while maintaining near-optimal sensing performance. We also show that local homodyne detection is essentially optimal, achieving quadratic scaling of precision with the total number of photons. We further analyze the impact of thermal noise in the preparation stage on both privacy and estimation precision. Our results pave the way for the development of practical, private distributed quantum sensing protocols in continuous-variable quantum networks.

arXiv:2509.22103•npj Quantum Information•May 21, 2026•2 citations

A no-go theorem for privacy in distributed sensing using Gaussian states

Jason L. Pereira, Damian Markham

In the discrete variable setting, entangled resource states allow a set of parties to learn a global function of a set of spatially separated systems, whilst keeping the local parameters of those systems completely private. In the continuous variable setting, distributed sensing has been carried out using Gaussian resource states, but without the same guarantees about privacy. Here, we show that perfect privacy is impossible to achieve for any distributed sensing protocol that uses Gaussian states as a resource. We also introduce a measure of relative privacy, bounding the degree to which any Gaussian distributed sensing protocol can keep local parameters hidden.

quant-pharXiv:2606.23796•Jun 24, 2026•0 citations

Universal Operational Privacy in Distributed Quantum Sensing

Min Namkung, Dong-Hyun Kim, Seongjin Hong +3 more

Privacy is a fundamental requirement in distributed quantum sensor networks, where multiple clients estimate spatially distributed parameters using shared quantum resources while interacting with potentially untrusted servers. Despite its importance, existing privacy conditions rely on idealized quantum bounds and do not fully capture the operational constraints imposed by realistic measurements. Here, we introduce a universal operational privacy framework for distributed quantum sensing, formulated in terms of the experimentally accessible Fisher information matrix and applicable to arbitrary protocols characterized by singular information structures. The proposed condition provides a protocol-independent criterion, ensuring that no information about individual parameters is accessible to untrusted parties. We further experimentally demonstrate that a distributed quantum sensing protocol employing fewer photons than the number of estimated parameters simultaneously satisfies the universal privacy condition and achieves Heisenberg-limited precision. Our results establish universal operational constraints governing privacy in distributed quantum sensor networks and provide a foundation for practical, privacy-preserving quantum sensing beyond full-rank regimes.

quant-pharXiv:2601.19206•Physical Review Applied•Jan 28, 2026•0 citations

Experimental Private Quantum Networked Sensing

Nicolas Laurent-Puig, Laura dos Santos Martins, Luis Bugalho +5 more

Entangling distant quantum sensors is a key application of future quantum networks, allowing for the estimation of global functions of local parameters, with precision that is not possible with stand-alone, individual, quantum sensors. However, with this advantage comes the risk of information leakage over the network via possible malicious parties. It is often particularly important that local parameters remain unknown and that only the global function is shared across the network. Recently, the notion of privacy has been introduced in this context, which ensures that only the agreed function of parameters is shared over the network, even when malicious parties control the network itself, whilst maintaining the estimation advantage. In this work, we introduce a noise-robust protocol for private quantum networked sensing, which we realise using a high-fidelity Greenberger-Horne-Zeilinger (GHZ) state source. We further run a comparative analysis and simulate attacks using three different quantum states, a four-qubit GHZ state, two Bell pairs, and a fully separable state. Our results highlight the clear advantage of GHZ states in maintaining high precision, accuracy, and privacy for the distributed estimation task.

quant-pharXiv:2609.16743•Sep 16, 2026•0 citations
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 analysing 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.
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.
Private distributed quantum sensing aims to estimate an authorized collective parameter while preventing independent estimation of individual local parameters. Here, we analytically characterize Gaussian quantum networks satisfying this perfect local privacy condition. Using a graph representation of the Gaussian pairing matrix, we show that two-mode squeezed vacuum states constitute the essential building blocks of privacy-preserving Gaussian states. We then analytically derive the optimal sensitivity under perfect local privacy and determine a Gaussian probe that achieves Heisenberg scaling with respect to both the photon number and the number of sensing modes. Using local homodyne measurements and maximum-likelihood estimation, we numerically verify quantum-enhanced sensitivity beyond the shot-noise limit while preserving perfect local privacy. We further show that the local-privacy condition is preserved under arbitrary phase-independent quantum channels, including optical loss. Our results provide a general framework for constructing and optimizing privacy-preserving continuous-variable quantum sensing networks.
We study the privacy properties of distributed quantum sensing protocols in a Gaussian quantum network, where each node encodes a parameter via a local phase shift. We first show that perfect privacy and optimal precision are jointly achievable using specifically tailored multimode photon-number correlated states. We then consider Gaussian states, which are experimentally less demanding as they can be implemented using only linear optics and two-photon parametric processes. Focusing on fully symmetric Gaussian states, we show that for networks with more than two nodes, perfect privacy can be achieved only asymptotically, in the limit of large photon numbers. However, we show that optimized fully-symmetric Gaussian states enable improved privacy levels while maintaining near-optimal sensing performance. We also show that local homodyne detection is essentially optimal, achieving quadratic scaling of precision with the total number of photons. We further analyze the impact of thermal noise in the preparation stage on both privacy and estimation precision. Our results pave the way for the development of practical, private distributed quantum sensing protocols in continuous-variable quantum networks.
In the discrete variable setting, entangled resource states allow a set of parties to learn a global function of a set of spatially separated systems, whilst keeping the local parameters of those systems completely private. In the continuous variable setting, distributed sensing has been carried out using Gaussian resource states, but without the same guarantees about privacy. Here, we show that perfect privacy is impossible to achieve for any distributed sensing protocol that uses Gaussian states as a resource. We also introduce a measure of relative privacy, bounding the degree to which any Gaussian distributed sensing protocol can keep local parameters hidden.
Privacy is a fundamental requirement in distributed quantum sensor networks, where multiple clients estimate spatially distributed parameters using shared quantum resources while interacting with potentially untrusted servers. Despite its importance, existing privacy conditions rely on idealized quantum bounds and do not fully capture the operational constraints imposed by realistic measurements. Here, we introduce a universal operational privacy framework for distributed quantum sensing, formulated in terms of the experimentally accessible Fisher information matrix and applicable to arbitrary protocols characterized by singular information structures. The proposed condition provides a protocol-independent criterion, ensuring that no information about individual parameters is accessible to untrusted parties. We further experimentally demonstrate that a distributed quantum sensing protocol employing fewer photons than the number of estimated parameters simultaneously satisfies the universal privacy condition and achieves Heisenberg-limited precision. Our results establish universal operational constraints governing privacy in distributed quantum sensor networks and provide a foundation for practical, privacy-preserving quantum sensing beyond full-rank regimes.
Entangling distant quantum sensors is a key application of future quantum networks, allowing for the estimation of global functions of local parameters, with precision that is not possible with stand-alone, individual, quantum sensors. However, with this advantage comes the risk of information leakage over the network via possible malicious parties. It is often particularly important that local parameters remain unknown and that only the global function is shared across the network. Recently, the notion of privacy has been introduced in this context, which ensures that only the agreed function of parameters is shared over the network, even when malicious parties control the network itself, whilst maintaining the estimation advantage. In this work, we introduce a noise-robust protocol for private quantum networked sensing, which we realise using a high-fidelity Greenberger-Horne-Zeilinger (GHZ) state source. We further run a comparative analysis and simulate attacks using three different quantum states, a four-qubit GHZ state, two Bell pairs, and a fully separable state. Our results highlight the clear advantage of GHZ states in maintaining high precision, accuracy, and privacy for the distributed estimation task.