Faithful and secure distributed quantum sensing under general-coherent attacks

F. Bruni; G. Bizzarri; I. Gianani; M. Barbieri; M. Manrique; M. Parisi; M. Rosati

REVIEW 5 major objections 4 minor 55 references

Faithful and secure distributed quantum sensing under general-coherent attacks

T0 review · 5 major / 4 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read The paper establishes that a threshold-based one-way protocol makes distributed quantum sensing perfectly secure against general-coherent attacks, with bias and variance deviations bounded by the safety threshold, and demonstrates this…

desk verdict The LOCC1 de Finetti application and threshold-based mechanism are worth a look, but Protocol 1 and Protocol 2 as written do not estimate the phase they claim to, so the central results do not hold. read the letter →

arxiv 2505.02620 v1 pith:CPWRVSDL submitted 2025-05-05 quant-ph math-phmath.MPphysics.optics

G. Bizzarri , M. Barbieri , M. Manrique , M. Parisi , F. Bruni , I. Gianani , M. Rosati This is my paper · ORCID

classification quant-phmath-phmath.MPphysics.optics

keywords distributedquantumsensingmetrologygeneral-coherentattacksmutuallyunbiasedbasesdeFinettitheoremphaseestimationentanglementsafetythreshold

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper proposes distributed quantum sensing protocols in which a quantum-capable provider sends probe states over a public network to a remote party who encodes an unknown phase, and the same rounds that estimate the phase also certify whether an eavesdropper has tampered with the probes. The central claim is that the one-way version is perfectly secure and faithful: if the fidelity measured in check rounds clears a safety threshold $\epsilon$, then the bias and variance of the phase estimate differ from the ideal by explicit bounds, even when Eve can launch general-coherent attacks, i.e., entangle probes across rounds and use a quantum memory. The guarantees are shown to hold equally for an equivalent mutually-unbiased-bases formulation, so entanglement is a convenience rather than a requirement, and the two-way version retains faithfulness but not security. A photonic proof-of-principle with one entangled pair per round confirms the protocol is practical and shows that the theoretical bounds tend to overestimate actual tampering. This matters because it replaces abort-on-any-error policies with a quantitative threshold, making secure remote sensing compatible with realistic noisy channels.

What carries the argument

The load-bearing object is Protocol 1, an entanglement-based round structure that splits transmissions into check rounds (no phase encoding, Pauli measurements on both sides) and estimation rounds (phase encoding, restricted Pauli measurements), with a discard probability $p_d$ that creates the slack needed against general-coherent attacks. The fidelity check (3) reconstructs $\hat F = (1+\langle X\otimes Z\rangle+\langle Z\otimes X\rangle+\langle Y\otimes Y\rangle)/4$ from sifted check rounds and compares it to $1-\epsilon^2$. The proof machinery has three pieces: Lemma 1, which shows Protocol 1 is equivalent to the MUB-based Protocol 2 under the threshold rescaling $\epsilon^2=3\bar\epsilon^2/2$; Theorem 2, the LOCC1 quantum de Finetti theorem, which bounds the distance between the collective tampered state and a mixture of independent identical states by $f(T,N_d,n)$; and Lemma 2, a gentle-measurement lemma that transfers the fidelity estimated on check rounds to estimation rounds. Theorem 4 then shows that closeness in LOCC1 distance uniformly bounds the expectation and variance of local observables, which is what turns the fidelity certificate into the bias and variance guarantees.

What would settle it

Run Protocol 1 with a tampering channel whose true fidelity is just below $1-\epsilon^2$ but whose finite-sample check estimates fluctuate above it; if accepted rounds produce bias or variance deviations larger than the bounds in Eqs. (5) and (6), the finite-sample guarantee fails. Equivalent analytic test: compute the sampling distribution of $\hat F$ and find a tampered state with true fidelity below threshold that passes the check with positive probability.

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Extended reading notes

Core claim

The paper's central result, Theorem 1, states that the one-way entanglement-based Protocol 1 is perfectly secure under general-coherent attacks and that its faithfulness is exactly governed by the safety threshold $\epsilon$. If the check-round fidelity estimate satisfies $\hat F \ge 1-\epsilon^2$, then for any unbiased phase estimator $\hat\phi$ the tampered-state expectation and variance deviate from the ideal-state values by $|\mathbb E\hat\phi-\mathbb E\hat\phi'| \le \epsilon_0/(n|\sin(2n\phi)|)$ and $|\Delta^2\hat\phi-\Delta^2\hat\phi'| \le (2\epsilon_0+\epsilon_0^2)/(n^2\sin^2(2n\phi))$, where $\epsilon_0 = \sqrt{\frac23\epsilon^2+4f(T,N_d,n)}$ with $f(T,N_d,n)=(T-N_d-1)\sqrt{n/(2N_d)}$; restricting Eve to individual attacks removes the $f$ term. The proof proceeds by (i) proving equivalence to a MUB-based protocol with a rescaled threshold $\epsilon^2=3\bar\epsilon^2/2$, (ii) using a one-way-adaptive (LOCC1) quantum de Finetti theorem to show that check-round fidelity controls the estimation-round state distance, and (iii) converting that distance into uniform bias and variance bounds via error propagation. The paper also proves that the two-way version has similar faithfulness bounds but cannot guarantee security. A photonic implementation with $n=1$ entangled photons found fidelity $0.937\pm0.017$, corresponding to $\epsilon=0.251\pm0.034$, and measured deviations well inside the predicted bounds.

Load-bearing premise

The safety-threshold step treats the fidelity estimated from a finite number of check rounds as the exact fidelity of the received state, and the theorem's bound contains no finite-sample confidence interval to cover estimation noise.

Editorial extensions

If this is right

A user can keep the protocol running in noisy conditions by choosing a finite threshold $\epsilon$; detection of non-zero errors no longer forces an abort, only a threshold violation does.
Providers can implement secure distributed sensing without distributing entanglement: the MUB version has the same guarantees with a rescaled threshold, so prepare-and-send hardware suffices.
The check-round fidelity certificate extends to the estimation rounds even when Eve stores probes in a quantum memory, as long as enough rounds are discarded to make $f(T,N_d,n)$ small.
In the two-way configuration a passive Bob can certify faithfulness, but security is impossible because Eve can interact with the probe both before and after phase encoding.
Experimental bias and variance deviations can lie far below the certified bounds, so the guarantees are conservative rather than tight.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

A finite-$T$ rigorous version of the protocol would need a confidence interval on $\hat F$; inserting such a term into $\epsilon_0$ would show how many check rounds are needed to make the threshold meaningful.
The gap between the certified bounds and the observed deviations is a testable target: if the tampered state is reconstructed, the exact bias and variance can be compared against the bounds to see how much slack comes from the trace-distance step.
The same LOCC1 de Finetti certificate should transfer to multi-user sensor networks and to continuous-variable phase estimation wherever a check/estimation round split with MUB-like measurements is available.
An adversary aware of the finite-sample issue could attempt to make check-round correlations pass the threshold by chance while corrupting estimation rounds, so quantifying the required $N_c$ is a concrete open problem.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Short take: the paper's big idea is useful, but its central protocols don't estimate the phase they claim to, so the headline result doesn't follow.

What's new: applying the LOCC1 de Finetti theorem to distributed quantum sensing is a legitimately fresh step, and the threshold-based, non-abort mechanism is a reasonable response to the zero-tolerance problem in earlier work. The experiment is honest: it reports that the theoretical bounds overestimate tampering, and it gives a public-data link. Those parts are worth acknowledging.

The problem is at the core. Protocol 1 prepares |ψ+> = (|00>+|11>)/√2. For that state with n=1, a direct calculation gives = -sin(2ϕ) and = sin(2ϕ), so the argument of arccos in Eq. (4) is identically zero; the estimator returns π/4 regardless of ϕ. At ϕ=0 it should return 0, so it fails even in the noiseless case. The fidelity check (3) is also wrong: for the ideal state, = -1, so F_hat = 0, not 1. Protocol 2 has the same disease: for every P in {±X,±Z}, the prepared eigenstate evolved under U(ϕ) gives

= cos(2ϕ), so Eq. (8) returns 2ϕ, not ϕ. The Appendix A identity (A4) is false for the state defined in Eq. (2). These are not typos; Theorem 1 and Theorem 5 are derived from these formulas. The finite-sample issue, using F_hat from a finite number of check rounds as if it were exact fidelity without a confidence interval, is real but secondary; the noiseless case already breaks the estimator.

I would like to see whether the framework can be repaired, for example by choosing a different probe or fixing the estimator. But as written the central claim is unsupported and the paper should be rejected in its current form. That said, the topic is important and the LOCC1-de Finetti application could be valuable if the state/estimator problem is solved, so I would not desk-reject it; I would send it to referees with the expectation that substantial revision is needed. For now, do not cite it.

Referee Report

5 major / 4 minor

Summary. The manuscript proposes two one-way distributed quantum sensing protocols (an entanglement-based Protocol 1 and a MUB-based Protocol 2) and their two-way variants, claiming threshold-based faithfulness and one-way security against general-coherent attacks. The theoretical analysis imports an LOCC1 de Finetti theorem to relate fidelity measured in check rounds to the state used in estimation rounds, and derives bias and variance bounds (Theorems 1 and 5). The paper also reports a photonic polarization experiment with n=1 and compares the theoretical bounds with measured bias and variance. The main claimed novelties are the safety-threshold mechanism, the entanglement/MUB equivalence, and robustness to collective attacks.

Significance. The problem addressed is timely, and the use of the LOCC1 de Finetti theorem of Ref. [25] is an appropriate technical instrument with the potential to bring distributed sensing security closer to QKD standards. The paper contains an experimental demonstration and a public data repository link, which is commendable. If the claims were correct, the threshold-based (non-aborting) approach would be a practical advance over abort-based protocols. However, the central theoretical claims are not established as written: the phase estimators in both protocols fail on the ideal states, and the fidelity check in Protocol 1 fails on the ideal state. These are load-bearing algebraic errors, not presentation issues, so the significance of the paper cannot be assessed on the basis of the current theoretical results.

major comments (5)

[Protocol 1, Eqs. (2) and (4)] The phase estimator does not estimate the phase of the state that Protocol 1 actually prepares. For n=1, applying U(phi)=e^{i phi Y} to register B of the ideal state (|00>+|11>)/sqrt(2) gives <X_A X_B>? Direct calculation with the stated convention gives <X_A Z_B> = sin(2 phi) and <Z_A X_B> = -sin(2 phi) (up to the overall sign convention for Y), so the argument of the arccosine in Eq. (4) is identically zero. Equation (4) therefore returns pi/4 for every phi, including phi=0, and the bias and variance bounds in Theorem 1 do not follow.
[Protocol 1, Eq. (3)] The fidelity check fails on the ideal check-round state. For (|00>+|11>)/sqrt(2) with no phase encoding, one obtains <X_A Z_B> = <Z_A X_B> = 0 and <Y_A Y_B> = -1 with the stated Pauli convention, so Eq. (3) gives F_hat = 0, not 1. Even with the opposite sign convention for Y, F_hat = 1/2, so the ideal state does not pass a threshold of 1 - epsilon^2 for reasonable epsilon. This makes the protocol's check step inconsistent with its own ideal resource.
[Protocol 2, Eq. (8)] The MUB-based estimator is also incorrect for the ideal states. For n=1, with U(phi)=e^{i phi Y}, a direct calculation gives <+X> = sin(2 phi), <-X> = +sin(2 phi), <+Z> = cos(2 phi), and <-Z> = -cos(2 phi), where each expectation is taken on the phase-encoded state prepared for the corresponding signed P. The average (1/4) sum_{P in {±X,±Z}} <P> is therefore sin(2 phi)/2, not cos(2 phi), and Eq. (8) returns pi/2 at phi=0. The factor-of-two discrepancy noted in the text's discussion is not the only problem; the estimator has the wrong functional form over the whole range.
[Appendix A, Eq. (A4)] The identity used in the proof of Lemma 1 is false. With the standard definitions |±> = (|0> ± |1>)/sqrt(2) and |R/L> = (|0> ± i|1>)/sqrt(2), neither (|+>|0> + |->|1>)/sqrt(2) nor (|R>|R> + |L>|L>)/sqrt(2) equals the state (|00>+|11>)/sqrt(2) defined in Eq. (2). The correct X-basis expansion is (|+>|+> + |->|->)/sqrt(2), and the R/L expansion differs by a sign. Since Eqs. (A1)-(A3) and the claimed equivalence of Protocols 1 and 2 rest on (A4), the reduction step in the proof of Theorem 1 is not valid.
[Theorem 3, Eq. (14)] The finite-sample issue is load-bearing and should be addressed even after the estimator inconsistencies are fixed. Equation (14) uses the point estimate F_hat_P obtained from a finite number N_c of check rounds as if it were the exact fidelity of the state used in estimation rounds. No confidence interval, finite-sample tail bound, or abort-probability penalty appears. Since F_hat_P is random, there is a nonzero probability that the check passes while the true fidelity is well below the threshold, so the deterministic bounds in Eqs. (5)-(6) and (29)-(30) do not hold for finite T as stated.

minor comments (4)

[Section III B] In the paragraph after Protocol 1, the expected numbers Nc ≈ pe T/3 and Ne ≈ pc T/3 appear to interchange the roles of pc (no-encoding/check rounds) and pe (encoding/estimation rounds); please correct the assignment of the probabilities.
[Section III A] The bold observables X, Y, Z are defined only on the two-dimensional subspace span{|0>,|1>}; for n>1 their action on the orthogonal complement is left unspecified, although they are used in physical expressions such as X_A ⊗ Z_B. Please specify the full operators or state explicitly that only the restrictions to that subspace are relevant.
[Section IV] The experimental text states that an additional plate rotation by an angle theta corresponds to a phase phi = 2 theta; the relation of this rotation to the definition U(phi) = e^{i phi Y} should be spelled out, since estimator (4) depends on the Y-eigenbasis convention.
[Figure 3] Figure 3 reports a retrieved phase that depends on theta, whereas Eq. (4) as written would return a constant independent of theta; please clarify which estimator was actually applied to the experimental data.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central bounds follow from an externally sourced LOCC1 de Finetti theorem and an independently measured fidelity, not from fitted or self-referential inputs.

full rationale

The derivation chain does not reduce to its own inputs. Theorem 1 is derived by reducing Protocol 1 to the MUB-based Protocol 2 (Lemma 1), then invoking the LOCC1 de Finetti theorem of Li and Smith [25] (Theorem 2) to bound the distance between check-round and estimation-round states (Theorem 3). The fidelity F_hat entering the bound is an independently measured quantity from check rounds; it is not fitted to the bias or variance data whose deviations are then bounded in Eqs. (5)-(6). Theorem 4 converts LOCC1-distance into expectation and variance differences using only bounded local observables, and Eq. (35) rescales by the derivative of the ideal expectation; none of these steps defines the conclusion into the premise. The experimental comparison in Figs. 3-4 evaluates the predicted bounds using the measured fidelity and reports that the bounds overestimate observed deviations; this is a falsifiable empirical check, not a re-labeling of the input. Self-citations [40]-[42] concern the Sagnac interferometer and phase-estimation methods and are not load-bearing for the security or faithfulness claims. The finite-sample use of F_hat as if it were the exact fidelity is a statistical rigor gap, but it is not circularity: the protocol's abort decision is based on an estimate, while the theorem's structure does not define faithfulness as the value produced by that estimate. The paper explicitly flags in Sec. V that quantifying metrological performance exclusively via cryptographic parameters may be fundamentally limited, which further supports a non-circular reading. The algebra of Eq. (A4) and the estimators is questionable, but that is an internal correctness issue, not a self-referential reduction.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The protocol rests on external de Finetti theory, an assumed attack model, a privacy assumption about Bob's outcomes, and an assumption that finite fidelity estimates are exact. In addition, the proof relies on a false algebraic identity (A4). These are the main premises a reader would need to accept or verify.

free parameters (2)

protocol probabilities p_e, p_c, p_d
User-chosen fractions for estimation, check, and discard rounds; not fitted to data, but they set the security-efficiency tradeoff and appear in the error term f(T,Nd,n).
safety threshold epsilon
User-chosen threshold in Protocol 1 step 5; enters Theorem 1 bounds; no optimal value is derived.

assumptions (5)

standard math LOCC1 quantum de Finetti theorem (Theorem 2) from Li and Smith [25]
Imported without proof; central to replacing the collective tampered state with a mixture of product states in Theorem 3.
domain assumption Eve's attack is a collective quantum channel acting on all T rounds, and the protocol's randomization renders the joint state permutation-invariant
Assumed in Section VI.A.2; needed to apply the de Finetti theorem; excludes attacks that break permutation symmetry before the protocol's own randomization.
domain assumption Bob's measurement outcomes are private and never reach Eve or the public classical channel
Used in the Theorem 5 security proof ('she cannot measure said state nor access Bob's measurement outcomes'); without it, Eve learns the phase from the outcome.
domain assumption The fidelity estimate F_hat from Nc check rounds is treated as the exact fidelity
Protocol 1 step 5 and Theorem 3 Eq. (14); no finite-sample confidence interval is included in the bounds.
ad hoc to paper Eq. (A4): |psi+> is equivalent to (|+>|0>+|->|1>)/sqrt(2) and to (|R>|R>+|L>|L>)/sqrt(2)
Used in Appendix A to prove Lemma 1 equivalence; the two expressions are not equal for the standard definitions, so the proof step is invalid.

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Cite this review

Pith. "Pith review of Faithful and secure distributed quantum sensing under general-coherent attacks." pith.science (2026). https://pith.science/paper/CPWRVSDL

@misc{pith2026250502620,
  author       = {Pith},
  title        = {Pith review of: Faithful and secure distributed quantum sensing under general-coherent attacks},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CPWRVSDL}},
  note         = {Machine review of arXiv:2505.02620}
}

read the original abstract

Quantum metrology and cryptography can be combined in a distributed and/or remote sensing setting, where distant end-users with limited quantum capabilities can employ quantum states, transmitted by a quantum-powerful provider via a quantum network, to perform quantum-enhanced parameter estimation in a private fashion. Previous works on the subject have been limited by restricted assumptions on the capabilities of a potential eavesdropper and the use of abort-based protocols that prevent a simple practical realization. Here we introduce, theoretically analyze, and experimentally demonstrate single- and two-way protocols for distributed sensing combining several unique and desirable features: (i) a safety-threshold mechanism that allows the protocol to proceed in low-noise cases and quantifying the potential tampering with respect to the ideal estimation procedure, effectively paving the way for wide-spread practical realizations; (ii) equivalence of entanglement-based and mutually-unbiased-bases-based formulations; (iii) robustness against collective attacks via a LOCC-de-Finetti theorem, for the first time to our knowledge. Finally, we demonstrate our protocols in a photonic-based implementation, observing that the possibility of guaranteeing a safety threshold may come at a significant price in terms of the estimation bias, potentially overestimating the effect of tampering in practical settings.

Figures

Figures reproduced from arXiv: 2505.02620 by the authors.

**Figure 2.** FIG. 2. Sketch of the experimental setup: photon pairs gen [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 4.** FIG. 4. Precision of phase estimation. Top: bias with respect [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗

Figures from the paper (1 more)

**Figure 3.** Figure 3: FIG. 3. Results of the phase estimation. Top: retrieved value [PITH_FULL_IMAGE:figures/full_fig_p006_3.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

55 extracted references · 40 canonical work pages

[25]

Kasai, Y

H. Kasai, Y. Takeuchi, H. Hakoshima, Y. Matsuzaki, and Y. Tokura, Anonymous Quantum Sensing, J. Phys. Soc. Japan 91, 10.7566/JPSJ.91.074005 (2022)

doi:10.7566/jpsj.91.074005 2022
[1]

Note that this is a combination of soundness and integrity as defined by [6]

Faithfulness The legitimate users can estimate how much Eve has tampered with the ideal probe state, and hence quantify how much the actual estima- tion bias and error deviate from the ideal ones. Note that this is a combination of soundness and integrity as defined by [6]

work page
[2]

Security The legitimate users can quantify how much information about the estimated parameter has leaked to Eve. We present both a single-way protocol, where the probe remains in Bob’s lab after phase-encoding, and a two-way protocol, where the probe is sent back to Alice for mea- surement, discussing how security cannot be guaranteed in the second case, ...

work page
[3]

The authors have im- plemented a secure link between two parties by means of a polarisation-entangled state, as in the scenario of Fig

based on the proposal in [3]. The authors have im- plemented a secure link between two parties by means of a polarisation-entangled state, as in the scenario of Fig. 1. The integrity of the communication link has been verified by quantum state tomography, and, from the knowledge of the state, it has been possible to derive a fiducial statistical model for...

work page
[4]

Fi- nanziamento di progetti presentati da giovani ricercatori

Security and faithfulness for MUB- and entanglement-based protocols We are now ready to prove the security and faithfulness of the MUB-based protocol: Theorem 5. The one-way MUB-based DQS Protocol 2 is perfectly secure and its faithfulness is determined by ϵ. Indeed, the difference of bias and variance of the unbi- ased estimator ˆϕ calculated on the idea...

work page 2023
[5]

1- & 2-way Individual Perfect (1w), None (2w) Abort-based No

work page
[6]

Tampering attack: disrupting the estimation pro- cedure by modifying the states transmitted on the quantum channel

work page
[7]

Leaking attack: extracting information about the estimation procedure, in order to estimate the value of the parameter. The performance of the protocol is measured in response to these two kinds of attacks: faithfulness quantifies the resilience to tampering attacks, and it can be measured by the distance of the ideal state from the tampered state after p...

work page

Show all 55 references

[8]

Let P ∈ {±X,±Y,±Z} be a Pauli-like observable,|P,±⟩ its±1-eigenvectors, and consider the MUB-based Protocol 2

MUB-based protocol The first step towards proving Theorem 1 is reducing it to a MUB-based protocol that randomizes the state sent to Bob. Let P ∈ {±X,±Y,±Z} be a Pauli-like observable,|P,±⟩ its±1-eigenvectors, and consider the MUB-based Protocol 2. This protocol does not requi...
[9]

The basic idea is that, if we look at a small part of a large 8 entangled system, this is approximately separable

Quantifying tampering under GC attacks The protocol’s faithfulness under GC attacks relies on a de-Finetti theorem for adaptive measurements. The basic idea is that, if we look at a small part of a large 8 entangled system, this is approximately separable. At variance with the...
[10]

In order to do this, we first have to show that the LOCC 1-distance can be used to bound the deviation of local observables on collective states

LOCC1 bounds on bias and variance The last step is to employ Theorem 3 to quantify how much the phase-estimation results using a tampered state differ from the ideal case, as measured by bias and vari- ance to the true phase. In order to do this, we first have to show that the...
[11]

T. J. Proctor, P. A. Knott, and J. A. Dunningham, Mul- tiparameter estimation in networked quantum sensors, Phys. Rev. Lett. 120, 080501 (2018)

2018
[12]

Giovannetti, S

V. Giovannetti, S. Lloyd, and L. Maccone, Advances in quantum metrology, Nat. Photonics 5, 222 (2011)

2011
[13]

P. Yin, Y. Takeuchi, W.-H. Zhang, Z.-Q. Yin, Y. Mat- suzaki, X.-X. Peng, X.-Y. Xu, J.-S. Xu, J.-S. Tang, Z.-Q. 11 Zhou, G. Chen, C.-F. Li, and G.-C. Guo, Experimen- tal Demonstration of Secure Quantum Remote Sensing, Phys. Rev. Appl. 14, 014065 (2020)

2020
[14]

Takeuchi, Y

Y. Takeuchi, Y. Matsuzaki, K. Miyanishi, T. Sugiyama, and W. J. Munro, Quantum remote sensing with asym- metric information gain, Phys. Rev. A 99, 022325 (2019)

2019
[15]

S. W. Moore and J. A. Dunningham, Secure quantum remote sensing without entanglement, AVS Quantum Sci. 5, 10.1116/5.0137260 (2023), arXiv:2302.03617

2023 arXiv
[16]

Huang, C

Z. Huang, C. Macchiavello, and L. Maccone, Crypto- graphic quantum metrology, Phys. Rev. A 99, 022314 (2019)

2019
[17]

Shettell, E

N. Shettell, E. Kashefi, and D. Markham, Cryptographic approach to quantum metrology, Phys. Rev. A 105, L010401 (2022)

2022
[18]

Rogers, Distributed optical-fibre sensing, Measure- ment Science and Technology 10, R75 (1999)

A. Rogers, Distributed optical-fibre sensing, Measure- ment Science and Technology 10, R75 (1999)

1999
[19]

H. Qi, S. Iyengar, and K. Chakrabarty, Distributed sen- sor networks—a review of recent research, Journal of the Franklin Institute 338, 655 (2001), distributed Sensor Networks for Real-time Systems with Adaptive C onfig- uration

2001
[20]

He and Q

Z. He and Q. Liu, Optical fiber distributed acoustic sen- sors: A review, Journal of Lightwave Technology39, 3671 (2021)

2021
[21]

A. Ukil, H. Braendle, and P. Krippner, Distributed tem- perature sensing: Review of technology and applications, IEEE Sensors Journal 12, 885 (2012)

2012
[22]

Comparison of different single-user DQS protocols in the literature with the ones proposed in this article

1- & 2-way Individual Perfect (1w), Zero-tolerance (2w) Abort-based No (trap code), Yes (Clifford code) TABLE I. Comparison of different single-user DQS protocols in the literature with the ones proposed in this article. Attacks are labelled according to the capabilities of th...
[23]

W. Ge, K. Jacobs, Z. Eldredge, A. V. Gorshkov, and M. Foss-Feig, Distributed quantum metrology with lin- ear networks and separable inputs, Phys. Rev. Lett. 121, 043604 (2018)

2018
[24]

Zhuang, Z

Q. Zhuang, Z. Zhang, and J. H. Shapiro, Distributed quantum sensing using continuous-variable multipartite entanglement, Phys. Rev. A 97, 032329 (2018)

2018
[26]

X. Guo, C. R. Breum, J. Borregaard, S. Izumi, M. V. Larsen, T. Gehring, M. Christandl, J. S. Neergaard- Nielsen, and U. L. Andersen, Distributed quantum sens- ing in a continuous-variable entangled network, Nature Physics 16, 281 (2020)

2020
[27]

Zhao, Y.-Z

S.-R. Zhao, Y.-Z. Zhang, W.-Z. Liu, J.-Y. Guan, W. Zhang, C.-L. Li, B. Bai, M.-H. Li, Y. Liu, L. You, J. Zhang, J. Fan, F. Xu, Q. Zhang, and J.-W. Pan, Field Demonstration of Distributed Quantum Sensing without Post-Selection, Phys. Rev. X 11, 031009 (2021)

2021
[28]

K´ om´ ar, E

P. K´ om´ ar, E. M. Kessler, M. Bishof, L. Jiang, A. S. Sørensen, J. Ye, and M. D. Lukin, A quantum network of clocks, Nature Physics 10, 582 (2014)

2014
[29]

W. He, C. Huang, R. Guan, Y. Chen, Z. Zhang, and K. Wei, Experimental secure entanglement-free quan- tum remote sensing over 50 km of optical fiber (2024), arXiv:2412.18837

2024 arXiv
[30]

D. Xie, C. Xu, J. Chen, and A. M. Wang, High- dimensional cryptographic quantum parameter estima- tion, Quantum Information Processing 17, 116 (2018)

2018
[31]

J. Ho, J. W. Webb, R. M. J. Brooks, F. Grasselli, E. Gauger, and A. Fedrizzi, Quantum-private distributed sensing (2024), arXiv:2410.00970

2024
[32]

Hassani, S

M. Hassani, S. Scheiner, M. G. Paris, and D. Markham, Privacy in networks of quantum sensors, Physical Review Letters 134, 10.1103/physrevlett.134.030802 (2025)

2025 doi
[33]

Shettell, M

N. Shettell, M. Hassani, and D. Markham, Private net- work parameter estimation with quantum sensors (2022)

2022
[34]

Bugalho, M

L. Bugalho, M. Hassani, Y. Omar, and D. Markham, Pri- vate and Robust States for Distributed Quantum Sensing (2024), arXiv:2407.21701

2024 arXiv
[35]

A. Zang, A. Kolar, A. Gonzales, J. Chung, S. K. Gray, R. Kettimuthu, T. Zhong, and Z. H. Saleem, Quantum Advantage in Distributed Sensing with Noisy Quantum Networks (2024), arXiv:2409.17089

2024 arXiv
[36]

Li and G

K. Li and G. Smith, Quantum de Finetti Theorem un- der Fully-One-Way Adaptive Measurements, Phys. Rev. Lett. 114, 160503 (2015)

2015
[37]

D.-H. Kim, S. Hong, Y.-S. Kim, Y. Kim, S.-W. Lee, R. C. Pooser, K. Oh, S.-Y. Lee, C. Lee, and H.-T. Lim, Dis- tributed quantum sensing of multiple phases with fewer photons, Nature Communications 15, 266 (2024)

2024
[38]

Pirandola, U

S. Pirandola, U. L. Andersen, L. Banchi, M. Berta, D. Bunandar, R. Colbeck, D. Englund, T. Gehring, C. Lupo, C. Ottaviani, J. L. Pereira, M. Razavi, J. Sham- sul Shaari, M. Tomamichel, V. C. Usenko, G. Val- lone, P. Villoresi, and P. Wallden, Advances in quan- tum cryptography...

2020 arXiv
[39]

Shettell and D

N. Shettell and D. Markham, Quantum metrology with delegated tasks, Phys. Rev. A 106, 052427 (2022)

2022
[40]

Bilkis, M

M. Bilkis, M. Rosati, and J. Calsamiglia, Reinforcement-learning calibration of coherent- state receivers on variable-loss optical channels, in 2021 IEEE Inf. Theory Work. (IEEE, 2021) pp. 1–6

2021
[41]

Rosati, Performance of Coherent Frequency-Shift Keying for Classical Communication on Quantum Chan- nels, in 2021 IEEE Int

M. Rosati, Performance of Coherent Frequency-Shift Keying for Classical Communication on Quantum Chan- nels, in 2021 IEEE Int. Symp. Inf. Theory (IEEE, 2021) pp. 902–905

2021
[42]

Rosati and A

M. Rosati and A. Solana, Joint-detection learning for op- tical communication at the quantum limit, Opt. Quan- tum 2, 390 (2024), arXiv:2312.13693

2024 arXiv
[43]

N¨ otzel and M

J. N¨ otzel and M. Rosati, Operating Fiber Networks in the Quantum Limit, J. Light. Technol. 41, 6865 (2023), arXiv:2201.12397

2023 arXiv
[44]

Munar-Vallespir and J

P. Munar-Vallespir and J. N¨ otzel, Joint communica- tion and sensing over the lossy bosonic quantum chan- nel, in 2024 IEEE 10th World Forum Internet Things (IEEE, 2024) pp. 1–6

2024
[45]

Renner, Symmetry of large physical systems implies independence of subsystems, Nat

R. Renner, Symmetry of large physical systems implies independence of subsystems, Nat. Phys. 3, 645 (2007), arXiv:0703069 [quant-ph]

2007
[46]

F. G. Brandao and A. W. Harrow, Quantum de finetti theorems under local measurements with applications, in Proc. forty-fifth Annu. ACM Symp. Theory Comput. (ACM, New York, NY, USA, 2013) pp. 861–870

2013
[47]

Winter, Coding theorem and strong converse for quan- tum channels, IEEE Trans

A. Winter, Coding theorem and strong converse for quan- tum channels, IEEE Trans. Inf. Theory 45, 2481 (1999), arXiv:1409.2536

1999 arXiv
[48]

N. K. Langford, T. J. Weinhold, R. Prevedel, K. J. Resch, A. Gilchrist, J. L. O’Brien, G. J. Pryde, and A. G. White, Demonstration of a simple entangling optical gate and its use in bell-state analysis, Phys. Rev. Lett. 95, 210504 (2005)

2005
[49]

Kiesel, C

N. Kiesel, C. Schmid, U. Weber, R. Ursin, and H. Wein- furter, Linear optics controlled-phase gate made simple, Phys. Rev. Lett. 95, 210505 (2005). 12

2005
[50]

Okamoto, H

R. Okamoto, H. F. Hofmann, S. Takeuchi, and K. Sasaki, Demonstration of an optical quantum controlled-not gate without path interference, Phys. Rev. Lett. 95, 210506 (2005)

2005
[51]

Bizzarri, I

G. Bizzarri, I. Gianani, M. Manrique, V. Be- rardi, F. Bruni, G. Capellini, and M. Barbi- eri, Quantum steering from phase measurements with limited resources, AVS Quantum Science 6, 024405 (2024), https://pubs.aip.org/avs/aqs/article- pdf/doi/10.1116/5.0205469/19956771/024405...

2024 doi
[52]

Bizzarri, S

G. Bizzarri, S. Gherardini, M. Manrique, F. Bruni, I. Gianani, and M. Barbieri, Quasiprobability distribu- tions with weak measurements (2024), arXiv:2406.06713 [quant-ph]

2024 arXiv
[53]

Bizzarri, M

G. Bizzarri, M. Parisi, M. Manrique, I. Gianani, A. Chi- uri, M. Rosati, V. Giovannetti, M. G. A. Paris, and M. Barbieri, Retrieving information in sloppy quantum phase estimation (2025), arXiv:2503.04976 [quant-ph]

2025
[54]

10.5281/zenodo.15271379

doi
[55]

Ac´ ın, Statistical Distinguishability between Uni- tary Operations, Phys

A. Ac´ ın, Statistical Distinguishability between Uni- tary Operations, Phys. Rev. Lett. 87, 177901 (2001), arXiv:0102064 [quant-ph]. Appendix A: Equivalence of entanglement- and MUB-based protocols Proof. (Proof of Lemma 1 ) In the entanglement-based protocol, Alice’s registe...

2001

Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.

[1] [25]

Kasai, Y

H. Kasai, Y. Takeuchi, H. Hakoshima, Y. Matsuzaki, and Y. Tokura, Anonymous Quantum Sensing, J. Phys. Soc. Japan 91, 10.7566/JPSJ.91.074005 (2022)

doi:10.7566/jpsj.91.074005 2022

[2] [1]

Note that this is a combination of soundness and integrity as defined by [6]

Faithfulness The legitimate users can estimate how much Eve has tampered with the ideal probe state, and hence quantify how much the actual estima- tion bias and error deviate from the ideal ones. Note that this is a combination of soundness and integrity as defined by [6]

work page

[3] [2]

Security The legitimate users can quantify how much information about the estimated parameter has leaked to Eve. We present both a single-way protocol, where the probe remains in Bob’s lab after phase-encoding, and a two-way protocol, where the probe is sent back to Alice for mea- surement, discussing how security cannot be guaranteed in the second case, ...

work page

[4] [3]

The authors have im- plemented a secure link between two parties by means of a polarisation-entangled state, as in the scenario of Fig

based on the proposal in [3]. The authors have im- plemented a secure link between two parties by means of a polarisation-entangled state, as in the scenario of Fig. 1. The integrity of the communication link has been verified by quantum state tomography, and, from the knowledge of the state, it has been possible to derive a fiducial statistical model for...

work page

[5] [4]

Fi- nanziamento di progetti presentati da giovani ricercatori

Security and faithfulness for MUB- and entanglement-based protocols We are now ready to prove the security and faithfulness of the MUB-based protocol: Theorem 5. The one-way MUB-based DQS Protocol 2 is perfectly secure and its faithfulness is determined by ϵ. Indeed, the difference of bias and variance of the unbi- ased estimator ˆϕ calculated on the idea...

work page 2023

[6] [5]

1- & 2-way Individual Perfect (1w), None (2w) Abort-based No

work page

[7] [6]

Tampering attack: disrupting the estimation pro- cedure by modifying the states transmitted on the quantum channel

work page

[8] [7]

Leaking attack: extracting information about the estimation procedure, in order to estimate the value of the parameter. The performance of the protocol is measured in response to these two kinds of attacks: faithfulness quantifies the resilience to tampering attacks, and it can be measured by the distance of the ideal state from the tampered state after p...

work page