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arxiv: 2509.22103 · v3 · submitted 2025-09-26 · 🪐 quant-ph · cond-mat.mes-hall

Privacy in Distributed Quantum Sensing with Gaussian Quantum Networks

Uesli Alushi , Roberto Di Candia This is my paper

Pith reviewed 2026-05-18 13:08 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.mes-hall
keywords distributed quantum sensingGaussian quantum networksprivacyphase estimationcontinuous-variable quantum systemsmultimode correlated stateshomodyne detection
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The pith

Perfect privacy and optimal sensing precision are achievable together with tailored multimode states in Gaussian quantum networks.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper investigates privacy in distributed quantum sensing, where multiple nodes in a network each measure a local phase shift using quantum light. It shows that specially designed multimode photon-number correlated states can deliver both complete protection against an eavesdropper and the best possible measurement accuracy. For more practical Gaussian states that are symmetric across the network, perfect privacy only becomes possible when the total number of photons is very large, but states can be optimized to get better privacy without losing much in sensing performance. The analysis also confirms that simple local measurements work nearly as well as more complex ones and examines how preparation noise affects the results.

Core claim

In Gaussian quantum networks for distributed sensing with local phase encoding at each node, perfect privacy and optimal precision can be achieved simultaneously using tailored multimode photon-number correlated states. For fully symmetric Gaussian states and networks larger than two nodes, perfect privacy is attainable only in the limit of large photon numbers. Optimized versions of these symmetric Gaussian states provide better privacy while keeping sensing performance close to optimal, and local homodyne detection achieves the expected quadratic scaling of precision with photon number. The effects of thermal noise during state preparation are also quantified for both privacy and precision

What carries the argument

Tailored multimode photon-number correlated states that encode sensing parameters while restricting an eavesdropper to a reduced view of the system after phase shifts.

If this is right

  • Perfect privacy requires asymptotically large photon numbers for symmetric Gaussian states in networks with more than two nodes.
  • Optimized fully symmetric Gaussian states improve privacy while keeping sensing near optimal.
  • Local homodyne detection is sufficient to reach quadratic precision scaling with total photon number.
  • Thermal noise introduced in state preparation reduces both the achievable privacy and the estimation precision.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • For small practical networks, moderate photon numbers with optimized states may be preferred over chasing perfect privacy.
  • The framework could guide secure multi-party quantum metrology designs that balance sensing and information protection.
  • Extending beyond Gaussian states might allow perfect privacy at smaller photon numbers in noisy conditions.

Load-bearing premise

The eavesdropper is assumed to have access only to the reduced state of the quantum system after the phase shifts are applied at each node.

What would settle it

An explicit calculation showing a finite-photon symmetric Gaussian state in a three-node network that reaches perfect privacy would falsify the asymptotic claim, or an experiment finding a measurement better than local homodyne that improves the scaling.

Figures

Figures reproduced from arXiv: 2509.22103 by Roberto Di Candia, Uesli Alushi.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
read the original abstract

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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript examines privacy in distributed quantum sensing protocols over Gaussian quantum networks, where each node encodes a local phase shift. It first demonstrates that perfect privacy and optimal precision can be jointly achieved using tailored multimode photon-number correlated states. For experimentally accessible fully symmetric Gaussian states prepared via linear optics and two-photon parametric processes, the authors show that perfect privacy in networks with more than two nodes is possible only asymptotically in the large-photon-number limit, while optimized states yield improved privacy alongside near-optimal sensing performance. Local homodyne detection is shown to be essentially optimal, delivering quadratic scaling of precision with total photon number. The impact of thermal noise during state preparation on both privacy and estimation precision is also analyzed.

Significance. If the central results hold under the stated model, this work offers a concrete route toward practical private distributed sensing in continuous-variable quantum networks by balancing privacy and metrological performance. The explicit construction of states achieving joint optimality, the asymptotic analysis for symmetric Gaussians, the optimality proof for local homodyne detection, and the thermal-noise robustness study constitute useful technical contributions to quantum metrology and quantum information security.

major comments (2)
  1. [Privacy definition and threat model (near the start of the Gaussian-states section)] The privacy metric and all optimality claims are defined with respect to an eavesdropper who receives only the reduced state after the local phase encodings (implicit in the Gaussian covariance-matrix treatment). This restricted threat model is load-bearing for the headline result that perfect privacy and optimal precision are jointly achievable. The manuscript should explicitly justify why channel-tapping attacks or retention of auxiliary/environment modes from the parametric sources are excluded, and state whether relaxing this assumption preserves the joint privacy-precision claim.
  2. [Fully symmetric Gaussian states analysis] For networks with N>2, the claim that perfect privacy is achievable only asymptotically requires an explicit derivation of the privacy metric (e.g., mutual information or Holevo quantity) as a function of mean photon number. The scaling that demonstrates the asymptotic limit should be shown in a dedicated equation or proposition rather than asserted from the covariance-matrix analysis alone.
minor comments (2)
  1. [Abstract] The abstract states that the authors 'show' the claims; a single sentence defining the precise privacy metric (e.g., accessible information to the eavesdropper) would improve clarity for readers.
  2. [State preparation section] Notation for the multimode photon-number correlated states and the symmetric Gaussian covariance matrices should be introduced with a brief table or explicit matrix form to aid reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major comment below and have revised the manuscript to improve clarity and rigor where appropriate.

read point-by-point responses

  1. Referee: [Privacy definition and threat model (near the start of the Gaussian-states section)] The privacy metric and all optimality claims are defined with respect to an eavesdropper who receives only the reduced state after the local phase encodings (implicit in the Gaussian covariance-matrix treatment). This restricted threat model is load-bearing for the headline result that perfect privacy and optimal precision are jointly achievable. The manuscript should explicitly justify why channel-tapping attacks or retention of auxiliary/environment modes from the parametric sources are excluded, and state whether relaxing this assumption preserves the joint privacy-precision claim.

    Authors: We thank the referee for this observation. Our model considers a passive eavesdropper who accesses only the reduced state on the modes available after the local phase encodings, as is standard in covariance-matrix treatments of Gaussian quantum networks. We exclude active channel-tapping during distribution and retention of auxiliary modes from the parametric sources because the protocol assumes trusted state preparation and distribution to the sensing nodes, with the eavesdropper limited to post-encoding interception. This is consistent with many continuous-variable quantum metrology analyses. We will add an explicit paragraph justifying the threat model in the revised Gaussian-states section. Relaxing the assumption to include channel tapping would generally allow the eavesdropper additional information, so the joint perfect-privacy/optimal-precision claim is specific to the considered model; our results nonetheless provide a useful benchmark for the restricted setting relevant to practical networks. Revision made: yes. revision: yes

  2. Referee: [Fully symmetric Gaussian states analysis] For networks with N>2, the claim that perfect privacy is achievable only asymptotically requires an explicit derivation of the privacy metric (e.g., mutual information or Holevo quantity) as a function of mean photon number. The scaling that demonstrates the asymptotic limit should be shown in a dedicated equation or proposition rather than asserted from the covariance-matrix analysis alone.

    Authors: We agree that an explicit derivation will enhance clarity. In the revised manuscript we will add a dedicated proposition (or equation) in the fully symmetric Gaussian states section that derives the privacy metric—specifically the Holevo information between the eavesdropper’s reduced covariance matrix and the vector of encoded phases—as an explicit function of the mean photon number per mode. For N>2 the expression shows that the Holevo quantity vanishes only in the infinite-photon-number limit, with leading-order scaling proportional to 1/M (where M is the total mean photon number), obtained directly from the symplectic eigenvalues of the relevant sub-block of the covariance matrix. This replaces the previous implicit assertion. Revision made: yes. revision: yes

Circularity Check

0 steps flagged

No circularity; claims follow from standard Gaussian-state calculations

full rationale

The paper's derivation relies on the covariance-matrix formalism for Gaussian states prepared via linear optics and parametric down-conversion, followed by local phase encoding and analysis of the eavesdropper's reduced state. Privacy and precision bounds are obtained from standard quantum estimation quantities (e.g., quantum Fisher information) applied to this model. No equations reduce a prediction to a fitted parameter by construction, no self-citation is load-bearing for the central result, and the asymptotic large-photon-number limit for perfect privacy is an explicit limiting case of the derived expressions rather than a definitional identity. The threat model (Eve sees only the post-encoding reduced state) is an upfront modeling choice, not a self-referential loop.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The claims rest on standard continuous-variable quantum optics and quantum parameter estimation theory; no free parameters, ad-hoc axioms, or invented entities are mentioned in the abstract.

axioms (2)
  • standard math Standard properties of Gaussian states under linear optics and parametric processes
    Invoked when restricting to Gaussian states that can be implemented with linear optics and two-photon processes.
  • domain assumption Quantum estimation theory bounds for phase sensing
    Used to claim optimal precision and quadratic scaling with total photon number.

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