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arxiv: 2606.23796 · v1 · pith:ZIJVW4YOnew · submitted 2026-06-22 · 🪐 quant-ph

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

Jason L. Pereira , Damian Markham This is my paper

Pith reviewed 2026-06-26 08:02 UTC · model grok-4.3

classification 🪐 quant-ph
keywords no-go theoremdistributed sensingGaussian statesprivacycontinuous variablesquantum information
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The pith

Perfect privacy cannot be achieved in any distributed sensing protocol that uses Gaussian states.

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

The paper establishes that while discrete-variable entangled states enable parties to learn global functions of spatially separated systems while keeping local parameters private, this is impossible with Gaussian states in the continuous-variable setting. It proves a no-go theorem showing that no such protocol using Gaussian resources can achieve perfect privacy. The authors also define a measure of relative privacy that bounds how much local information can be hidden in any Gaussian protocol.

Core claim

No distributed sensing protocol using Gaussian resource states can achieve perfect privacy, meaning that local parameters cannot be completely hidden from all parties while learning a global function of the systems.

What carries the argument

The no-go theorem showing that Gaussian states cannot satisfy the privacy conditions for distributed sensing, together with the introduced relative privacy measure.

If this is right

  • Any protocol using Gaussian states will leak some information about local parameters to the parties.
  • A relative privacy measure can bound the achievable privacy in Gaussian protocols.
  • Achieving perfect privacy requires resource states beyond Gaussian ones.

Where Pith is reading between the lines

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

  • This implies that non-Gaussian states should be explored for privacy-preserving distributed sensing.
  • Hybrid discrete-continuous variable protocols might combine the advantages of both.
  • The result limits the use of common Gaussian resources like squeezed states in secure sensing applications.

Load-bearing premise

The protocols are restricted to Gaussian resource states and privacy requires that local parameters remain completely hidden from all parties.

What would settle it

A concrete counterexample of a Gaussian-state distributed sensing protocol that achieves complete hiding of local parameters while learning the global function would falsify the theorem.

Figures

Figures reproduced from arXiv: 2606.23796 by Damian Markham, Jason L. Pereira.

Figure 1
Figure 1. Figure 1: FIG. 1: The basic setup for a distributed sensing [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: An illustration of the necessary condition for [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Privacy can be restored in a trivial way by [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
read the original abstract

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.

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

0 major / 3 minor

Summary. The manuscript establishes a no-go theorem proving that perfect privacy—defined as learning a global function of spatially separated systems while keeping all local parameters completely hidden—cannot be achieved by any distributed sensing protocol that employs Gaussian states as resources in the continuous-variable setting. This is contrasted with the discrete-variable case where entangled resources permit such privacy. The authors additionally introduce and analyze a relative privacy measure that quantifies the maximum privacy achievable under Gaussian constraints.

Significance. If the central derivation holds, the result is significant for continuous-variable quantum metrology: Gaussian states are experimentally accessible and widely employed, yet the theorem shows they are fundamentally insufficient for perfect privacy in distributed sensing tasks. The relative privacy measure supplies a concrete, quantitative bound that can guide protocol design and highlights the necessity of non-Gaussian resources when privacy is required. The work therefore supplies both a negative result and a practical diagnostic tool.

minor comments (3)
  1. [Abstract] The abstract introduces the relative privacy measure without a one-sentence characterization of its functional form or normalization; adding this would improve immediate readability.
  2. Notation for the privacy measure (e.g., any subscript or argument indicating the global function versus local parameters) should be introduced explicitly at its first appearance in the main text.
  3. Figure captions should explicitly state whether plotted curves correspond to the relative privacy bound derived in the theorem or to numerical examples.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of our manuscript and for recommending minor revision. No major comments were raised, indicating that the central no-go theorem and the relative privacy measure are viewed as sound. We will address any minor points in the revised version.

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper establishes a no-go theorem for perfect privacy in Gaussian-state distributed sensing via direct analysis of covariance matrices and measurement outcomes in the continuous-variable setting. The derivation relies on standard properties of Gaussian states (e.g., symplectic transformations and partial traces) and a privacy definition that requires local parameters to be information-theoretically hidden while a global function is learned; neither the theorem statement nor the relative-privacy measure reduces to a fitted parameter, self-citation chain, or definitional loop. The argument is scoped explicitly to Gaussian resources and contrasts with the discrete-variable case without importing uniqueness results from the authors' prior work. No load-bearing step equates a prediction or claim to its own inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

Only the abstract is available, so the ledger is populated from the stated claims. No explicit free parameters or invented entities are described beyond the relative privacy measure.

axioms (2)
  • domain assumption Gaussian states are the only resource states considered for the distributed sensing protocols
    The claim is restricted to Gaussian states as stated in the abstract.
  • domain assumption Privacy requires that local parameters remain completely hidden while the global function is learned
    This is the privacy guarantee contrasted with the discrete-variable case in the abstract.
invented entities (1)
  • relative privacy measure no independent evidence
    purpose: To bound the degree to which Gaussian protocols can keep local parameters hidden
    Introduced in the abstract as a new quantification tool when perfect privacy is impossible.

pith-pipeline@v0.9.1-grok · 5610 in / 1178 out tokens · 23219 ms · 2026-06-26T08:02:13.834417+00:00 · methodology

discussion (0)

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Reference graph

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