Trusted Repeater Placement in QKD-enabled Optical Networks

Arup Kumar Marik; Basabdatta Palit; Sadananda Behera

REVIEW 4 major objections 5 minor 13 references

Trusted repeater placement can be guided by a composite centrality score computed on a reliability-weighted network, and the paper shows this beats degree centrality by 10.77 percentage points of shortest-path coverage on a 28-node metro to

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A reliability-weighted composite of betweenness and eigenvector centrality ranks trusted repeater nodes in QKD networks, yielding 10.77% more shortest-path coverage than degree centrality at K=8.

T0 review reviewed 2026-08-04 challenge →

load-bearing objection A reasonable heuristic, but the main claim is not supported: the only baseline is degree centrality, so the 10.77% gain may just be betweenness centrality rediscovered. the 4 major comments →

arxiv 2509.10338 v1 pith:CDRX4BFT submitted 2025-09-12 cs.NI

Trusted Repeater Placement in QKD-enabled Optical Networks

Arup Kumar Marik , Basabdatta Palit , Sadananda Behera This is my paper

classification cs.NI

keywords Quantum Key DistributionTrusted Repeater NodeNode ReliabilityBetweenness CentralityEigenvector CentralityCumulative Path CoverageMetro Optical NetworkDijkstra Shortest Path

verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

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 tries to solve a placement problem: given a QKD-enabled optical network where some nodes may be less trustworthy, where should a limited number of trusted repeater nodes (TRNs) be put so that as many end-to-end shortest paths as possible can relay keys securely? The authors propose a two-part heuristic: modify the link weights used by Dijkstra's algorithm so that shortest paths favor nodes with higher reliability scores, then rank each node by a composite score that averages betweenness centrality and eigenvector centrality computed on that reliability-modified graph. They test the ranking on a 28-node metro topology with reliability scores drawn uniformly from [0.5, 1], and report that selecting the top eight nodes by this composite score covers 10.77 percentage points more of the network's shortest paths than selecting the top eight by degree centrality (58.37% versus 47.60%). If correct, this gives network planners a generic, cheap way to pick TRN locations that jointly accounts for structural importance and security risk.

Core claim

The central claim is that a composite centrality metric computed on a reliability-weighted graph identifies trusted repeater locations more effectively than degree centrality. For a graph G, each node v carries a reliability R_v in [0.5,1]. The paper replaces each link weight with w'_{uv} = α d'_{uv} + (1-α)/(R_u R_v), taking α=0.5, where d'_{uv} is the physical distance normalized by the longest link. It then computes betweenness centrality BC_v and eigenvector centrality EC_v on this modified graph, averages them over 1000 random reliability assignments, and ranks nodes by TS_v = 0.5 BC_v + 0.5 EC_v. On the 28-node metro network, the top eight nodes by this total score cover 58.37% of all

What carries the argument

The load-bearing object is the reliability-modified link weight, w'_{uv} = α d'_{uv} + (1-α)/(R_u R_v), which turns a simple distance-weighted graph into a 'trust-weighted' graph where paths that go through less reliable nodes incur a penalty. On this modified graph, the paper computes betweenness centrality (the fraction of shortest paths passing through a node) and eigenvector centrality (influence based on the centrality of neighbors), then forms the composite total score TS_v = β BC_v + (1-β) EC_v. Dijkstra's algorithm on the modified graph generates the shortest paths used both to compute centralities and to measure cumulative path coverage (CPC), the percentage of all shortest paths pa

Load-bearing premise

The entire advantage rests on the assumption that the particular weighting formula in Eq. (1), with α=0.5, correctly trades off physical distance against node reliability during path selection; the paper states this formula without deriving it or testing alternative values.

What would settle it

Rerun the 28-node simulation for several values of α (for example 0.2, 0.5, 0.8) while keeping everything else the same, and check whether the top-8 cumulative path coverage still beats degree centrality by a comparable margin; if the advantage narrows sharply or flips sign at other α, then the claimed gain is a property of the chosen weight rather than of the composite-score approach itself.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

For a fixed budget of about eight TRNs, the proposed ranking covers 10.77 percentage points more shortest paths than degree centrality; the advantage is smaller when K is very small or very large.
Baking reliability into the link weight steers shortest paths away from untrusted nodes, so the selected TRN set tends to consist of nodes that are both well-connected and relatively secure.
The procedure uses only an undirected graph, link distances, and per-node reliability scores, so it transfers to any topology where these data are available.
Coverage saturates after roughly 12 nodes, which implies that beyond a small number of TRNs additional placements yield diminishing returns for shortest-path coverage.

Where Pith is reading between the lines

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

The paper fixes α=β=0.5 and never varies them, so the reported 10.77-point gain may depend on those specific weights; a sensitivity analysis over α (and β) is needed to know whether the ranking advantage is robust or an artifact of the chosen weighting.
The evaluation optimizes a structural proxy—how many shortest paths touch a TRN—not actual secure key rate or end-to-end security; a natural next experiment is simulating key establishment and checking whether the coverage gain translates into higher key throughput.
Because reliability scores are averaged over random instances, the resulting ranking reflects average reliability rather than any specific real-world reliability profile; for a concrete deployment, ranking under that deployment's actual reliability values would be the more direct guideline.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

A reasonable heuristic, but the main claim is not supported: the only baseline is degree centrality, so the 10.77% gain may just be betweenness centrality rediscovered.

read the letter

You should know up front: the idea is sensible and the paper is clearly written, but the central claim is not established by the evidence as presented. The 10.77% coverage gain over degree centrality at K=8 is real in their simulation, but degree centrality is a weak baseline for path coverage, and nothing else is compared.

What's new is the specific combination: incorporating node reliability into link weights (Eq. 1) and then ranking candidate TRNs by a composite of betweenness and eigenvector centrality computed on those modified weights. That exact combination isn't in the cited TRN placement work, so it's a legitimate heuristic contribution. The problem is well motivated—QKD repeaters handle key material, so their trustworthiness matters. The algorithm is simple and clear; the pseudocode is easy to follow.

The soft spots are load-bearing. First, the comparison is only against degree centrality. Betweenness centrality is the standard baseline for "which nodes lie on many shortest paths," and their composite score is mostly a centrality measure. Without an ablation separating the BC component, the EC component, and the reliability weighting (α=0.5 vs α=0/α=1), you cannot attribute the gain to the reliability-aware mechanism. It might be that plain BC on the original graph reaches the same coverage; the paper doesn't tell us. Second, CPC is defined on "all shortest paths in the network," but they don't say whether those paths are computed on the original graph or the reliability-modified graph. If original, then exact BC on the original graph is the obvious baseline and it's missing; if modified, then the comparison against degree centrality is apples-to-oranges. Third, the evaluation is a single 28-node topology, with 1000 random reliability assignments but no error bars or significance test. The 10.77% could be within noise. Minor: α and β are set to 0.5 with no sensitivity analysis, and there's no comparison with any prior TRN placement method (e.g., the MILPs in [7] and [10]).

Who is this for? Researchers working on QKD network planning who want a quick heuristic. It's a solid starting point but needs a revised evaluation.

Recommendation: I would send it for peer review because the idea is worth engaging and the flaws are addressable, but I would tell the authors to add missing baselines (plain BC, eigenvector, degree, random), report variance across reliability instances, and analyze α/β sensitivity. Without that, the central claim should not be taken at face value.

Referee Report

4 major / 5 minor

Summary. The paper addresses trusted repeater node (TRN) placement in QKD-enabled metro optical networks when nodes have heterogeneous trustworthiness. It assigns each node a reliability score R_v in [0.5,1], modifies link weights as w'_uv = α·d'_uv + (1−α)/(R_u·R_v) in Eq. (1), recomputes shortest paths on this modified graph, and then ranks nodes by a composite score TS_v = β·BC_v + (1−β)·EC_v in Eq. (4). The top-K nodes are proposed as TRN locations. The method is evaluated on a 28-node, 52-link metro topology using 1000 random reliability assignments, and the paper reports that at K=8 the proposed ranking covers 10.77% more shortest paths than a degree-centrality baseline (58.37% vs 47.60% cumulative path coverage).

Significance. If the claimed improvement is robust, the paper would offer a simple, scalable heuristic for TRN placement that accounts for both node trustworthiness and topological importance, which is a relevant gap in the QKD network planning literature. The problem is well motivated, and the proposed two-step approach is easy to implement. However, the evidence for the central claim is currently weak: the comparison is limited to one topology, one baseline, and no ablation or statistical characterization. The paper would be strengthened considerably by adding missing baselines, sensitivity analysis, and uncertainty quantification.

major comments (4)

[§III.A, Eq. (1), Eq. (4)] The central claim that the 'reliability-aware composite score' improves TRN selection is not supported by the comparison against degree centrality alone. Degree centrality is a deliberately weak baseline for path coverage, and TS_v is dominated by betweenness centrality (β=0.5) computed on reliability-modified weights. Without an ablation that isolates (i) plain BC, (ii) plain EC, (iii) the composite without reliability-weighting (α=0 or α=1), and (iv) a random baseline, the 10.77% gain could be entirely due to rediscovering betweenness centrality rather than to the proposed reliability-aware mechanism. This comparison is load-bearing because the abstract claims the method 'covers 10.77% more shortest paths compared to traditional metrics like degree centrality,' not merely that it beats degree centrality.
[§III, Fig. 2 and Fig. 3] The definition of Cumulative Path Coverage is ambiguous. The text says CPC is 'the percentage of all shortest paths in the network that pass through at least one of the top-ranked TRN nodes,' but it does not specify whether these shortest paths are computed on the original physical link distances or on the reliability-modified weights w'_uv. If CPC uses original shortest paths, then ranking nodes by centralities computed on modified weights may be inconsistent with the evaluation objective. If CPC uses modified shortest paths, then the relevance of the metric to actual QKD routing needs justification. This must be clarified because the reported 58.37% vs 47.60% numbers only have meaning relative to a well-defined path set.
[§III, Algorithm 1] The statistical basis for the central claim is thin. The paper averages BC_v and EC_v over 1000 random reliability assignments and then ranks nodes, but no variance, confidence interval, or significance test is reported for the 10.77% gap. It is also unclear whether CPC is computed per reliability instance and then averaged, or computed once after averaging the scores. A single 28-node topology with no error bars leaves open the possibility that the improvement is within the noise of the random reliability draws. The authors should report the distribution of CPC differences across instances or at least a confidence interval, and ideally test on additional topologies.
[§II-A, Eq. (4)] The reliance on Eq. (1) and Eq. (4) without sensitivity or scale analysis is a correctness risk. The weight formula w'_uv = α·d'_uv + (1−α)/(R_u·R_v) is asserted without derivation, and α=0.5 is fixed; a different α could change the ranking and possibly eliminate the claimed gain. More importantly, BC_v and EC_v have different scales (BC can range over orders of magnitude, EC is eigenvector-scaled), and Eq. (4) combines them as a raw sum. Without normalization, the composite score may be dominated by whichever centrality has larger numerical values, making the β=0.5 choice effectively arbitrary. The authors should either normalize BC and EC before combination or justify the scale-compatibility of the two terms.

minor comments (5)

[§III] The text says 'The final Total Score TS_v is calculated using the average values of BC_v and EC_v over all instances,' but Algorithm 1 describes computing scores per instance. Clarify whether the ranking is based on averaged scores or on per-instance rankings combined afterwards.
[§II-A, Eq. (1)] The normalization of d'_uv is only described verbally as being with respect to the maximum link distance. Provide the explicit formula for d'_uv so the weight modification is reproducible.
[§II-B, Eq. (3)] In the eigenvector centrality definition, x_t is not defined and it is unclear whether the adjacency matrix is the binary adjacency of G' or the weighted adjacency with entries w'_uv. Please define all symbols.
[§II-A] The sentence 'A minimum threshold of 0.5 indicates the highest uncertainty in the security of the node' is confusing: a reliability of 0.5 means maximum uncertainty, but 'highest uncertainty' might be misread as a property of the threshold rather than the value. Reword for clarity.
[Fig. 3] The y-axis label of Fig. 3 is not described in the text. If the plot shows the difference in CPC, the axis should be labeled 'CPC difference (%)' rather than 'CPC (%).'

Circularity Check

0 steps flagged

No significant circularity: the ranking is not fitted to the CPC objective, no self-citation is load-bearing, and the central comparison is against an external baseline.

full rationale

The paper does not fit any parameter to the CPC target. The tunable parameters α and β are fixed at 0.5, and node reliabilities are drawn randomly and averaged over 1000 instances, so the ranking is not calibrated to the coverage metric. The central claim compares the proposed composite score against an external baseline (degree centrality), which is not derived from the proposed method and therefore provides an independent reference point. The only potentially self-referential element is that BC_v is defined as the fraction of shortest paths through v on the modified graph G', while CPC measures the fraction of shortest paths covered by the top-K set. If CPC were computed on the same G' shortest paths used to derive BC, then BC would act as a per-node proxy for the same path-coverage objective, making the ranking partly self-referential. However, the paper never explicitly states that CPC uses the modified graph; it says 'percentage of all shortest paths in the network,' which naturally reads as the original topology. Even if the modified graph were used, the composite score with EC and the union-based CPC are not identical functions, and the comparison against degree centrality remains a valid external benchmark. The paper also contains no self-citations that carry the argument: all references are prior external work, and Eq. (1) is presented as an asserted design choice rather than derived from the evaluation target. The missing BC-only ablation and the ambiguous CPC path basis are correctness/ablation concerns, not circularity.

Axiom & Free-Parameter Ledger

2 free parameters · 3 axioms · 0 invented entities

The framework introduces two hand-chosen weights (α, β) and relies on the unverified assumption that the reliability-weighted composite centrality identifies optimal TRN locations. No new physical entities are introduced.

free parameters (2)

alpha (α) = 0.5
Balancing parameter between normalized distance and reliability in link weight (Eq. 1). Chosen as equal weight; no sensitivity analysis or fitting.
beta (β) = 0.5
Balancing parameter between betweenness and eigenvector centrality in total score (Eq. 4). Chosen arbitrarily; no optimization or sensitivity analysis.

axioms (3)

domain assumption The QKD metro network can be modeled as an undirected graph where each node has a static reliability score R_v in [0.5,1].
The model abstracts away physical-layer QKD specifics, traffic, and time-varying trust; real trust scores are likely dynamic and correlated.
ad hoc to paper The reliability-aware link weight in Eq. (1), w' = α d' + (1-α)/(R_u R_v), with α=0.5, is a valid measure of link quality for key relay.
The functional form is not derived from a security or physics model; no sensitivity analysis is provided for α.
ad hoc to paper Nodes with high composite score TS_v = β BC_v + (1-β) EC_v are the best TRN candidates.
The paper provides no proof or benchmark showing that this composite maximizes path coverage; it is a heuristic premise.

reviewed 2026-08-04 · how reviews work

0 comments

Cite this review

Pith. "Pith review of Trusted Repeater Placement in QKD-enabled Optical Networks." pith.science (2026). https://pith.science/paper/CDRX4BFT

@misc{pith2026250910338,
  author       = {Pith},
  title        = {Pith review of: Trusted Repeater Placement in QKD-enabled Optical Networks},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CDRX4BFT}},
  note         = {Machine review of arXiv:2509.10338}
}

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read the original abstract

Quantum Key Distribution (QKD) provides information-theoretic security, but is limited by distance in optical networks, thereby requiring repeater nodes to extend coverage. Existing works usually assume all repeater nodes and associated Key Management Servers (KMSs) to be Trusted Repeater Nodes (TRNs), while ignoring risks from software exploits and insider threats. In this paper, we propose a reliability-aware TRN placement framework for metro optical networks, which assigns each node a trust score and integrates it into the Dijkstra algorithm via weighted links. We then rank the nodes using a composite score, which is a weighted combination of betweenness centrality and eigenvector centrality to enable a secure and scalable TRN deployment. Simulation results on a reference topology show that our method covers 10.77% more shortest paths compared to traditional metrics like degree centrality, using the same number (around eight) of TRNs, making it suitable for TRN selection to maximize secure connectivity.

Figures

Figures reproduced from arXiv: 2509.10338 by Arup Kumar Marik, Basabdatta Palit, Sadananda Behera.

**Figure 2.** Figure 2: Cumulative path coverage (CPC) by TRNs according to total score. [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

discussion (0)

Reference graph

Works this paper leans on

13 extracted references

[1]

Quantum key distribution secured optical networks: A survey,

P. Sharmaet al., “Quantum key distribution secured optical networks: A survey,”IEEE Open Journal of the Communications Society, vol. 2, pp. 2049–2083, 2021

2049
[2]

Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer,

P. W. Shor, “Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer,”SIAM review, vol. 41, no. 2, pp. 303–332, 1999

1999
[3]

Quantum cryptography: Public key distribution and coin tossing,

C. H. Bennettet al., “Quantum cryptography: Public key distribution and coin tossing,”Theoretical Comp. Sc., vol. 560, pp. 7–11, 2014

2014
[4]

Challenges of routing in quantum key distribution networks with trusted nodes for key relaying,

P.-Y . Kong, “Challenges of routing in quantum key distribution networks with trusted nodes for key relaying,”IEEE Comm. Mag., vol. 62, no. 7, pp. 124–130, 2023

2023
[5]

Secret key rate over multiple relays in quantum key distribution for cyber–physical systems,

——, “Secret key rate over multiple relays in quantum key distribution for cyber–physical systems,”IEEE Trans. on Ind. Informatics, vol. 20, no. 7, pp. 9599–9609, 2024

2024
[6]

Designing a quantum key distribution network- methodology and challenges,

M. Gunkelet al., “Designing a quantum key distribution network- methodology and challenges,” inPhotonic Networks; 20th ITG- Symposium. VDE, 2019, pp. 1–3

2019
[7]

Optimal design of practical quantum key distribu- tion backbones for securing coretransport networks,

F. Pederzolliet al., “Optimal design of practical quantum key distribu- tion backbones for securing coretransport networks,”Quantum Reports, vol. 2, no. 1, pp. 114–125, 2020

2020
[8]

Trusted node deployment strategies for long-haul quantum key distribution networks,

S. K. Patriet al., “Trusted node deployment strategies for long-haul quantum key distribution networks,” inIEEE ONDM, 2023, pp. 1–6

2023
[9]

Designing quantum networks using preexisting infras- tructure,

J. Rabbieet al., “Designing quantum networks using preexisting infras- tructure,”npj Quantum Information, vol. 8, no. 1, p. 5, Jan 2022

2022
[10]

A two-step linear programming approach for repeater placement in large-scale quantum networks,

R. Sripotchanartet al., “A two-step linear programming approach for repeater placement in large-scale quantum networks,”Computer Networks, vol. 254, p. 110795, 2024

2024
[11]

Cost-Efficient Network Planning for Quantum Commu- nication Infrastructure,

I. Maityet al., “Cost-Efficient Network Planning for Quantum Commu- nication Infrastructure,” inIEEE Globecom Wkshps, 2023, pp. 1039– 1044

2023
[12]

Traffic-Aware Trusted Node Placement and Re- source Allocation in Multi-Band EONs Secured With QKD,

M. R. Dibajet al., “Traffic-Aware Trusted Node Placement and Re- source Allocation in Multi-Band EONs Secured With QKD,”Journal of Lightwave Tech., vol. 43, no. 1, pp. 6–18, 2025

2025
[13]

Tidal-traffic-aware routing and spectrum allocation in elastic optical networks,

B. Yanet al., “Tidal-traffic-aware routing and spectrum allocation in elastic optical networks,”Journal of Optical Commun. and Netw., vol. 10, no. 11, pp. 832–842, 2018

2018

This paper was first reviewed by deepseek-v4-flash on August 4, 2026.

[1] [1]

Quantum key distribution secured optical networks: A survey,

P. Sharmaet al., “Quantum key distribution secured optical networks: A survey,”IEEE Open Journal of the Communications Society, vol. 2, pp. 2049–2083, 2021

2049

[2] [2]

Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer,

P. W. Shor, “Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer,”SIAM review, vol. 41, no. 2, pp. 303–332, 1999

1999

[3] [3]

Quantum cryptography: Public key distribution and coin tossing,

C. H. Bennettet al., “Quantum cryptography: Public key distribution and coin tossing,”Theoretical Comp. Sc., vol. 560, pp. 7–11, 2014

2014

[4] [4]

Challenges of routing in quantum key distribution networks with trusted nodes for key relaying,

P.-Y . Kong, “Challenges of routing in quantum key distribution networks with trusted nodes for key relaying,”IEEE Comm. Mag., vol. 62, no. 7, pp. 124–130, 2023

2023

[5] [5]

Secret key rate over multiple relays in quantum key distribution for cyber–physical systems,

——, “Secret key rate over multiple relays in quantum key distribution for cyber–physical systems,”IEEE Trans. on Ind. Informatics, vol. 20, no. 7, pp. 9599–9609, 2024

2024

[6] [6]

Designing a quantum key distribution network- methodology and challenges,

M. Gunkelet al., “Designing a quantum key distribution network- methodology and challenges,” inPhotonic Networks; 20th ITG- Symposium. VDE, 2019, pp. 1–3

2019

[7] [7]

Optimal design of practical quantum key distribu- tion backbones for securing coretransport networks,

F. Pederzolliet al., “Optimal design of practical quantum key distribu- tion backbones for securing coretransport networks,”Quantum Reports, vol. 2, no. 1, pp. 114–125, 2020

2020

[8] [8]

Trusted node deployment strategies for long-haul quantum key distribution networks,

S. K. Patriet al., “Trusted node deployment strategies for long-haul quantum key distribution networks,” inIEEE ONDM, 2023, pp. 1–6

2023

[9] [9]

Designing quantum networks using preexisting infras- tructure,

J. Rabbieet al., “Designing quantum networks using preexisting infras- tructure,”npj Quantum Information, vol. 8, no. 1, p. 5, Jan 2022

2022

[10] [10]

A two-step linear programming approach for repeater placement in large-scale quantum networks,

R. Sripotchanartet al., “A two-step linear programming approach for repeater placement in large-scale quantum networks,”Computer Networks, vol. 254, p. 110795, 2024

2024

[11] [11]

Cost-Efficient Network Planning for Quantum Commu- nication Infrastructure,

I. Maityet al., “Cost-Efficient Network Planning for Quantum Commu- nication Infrastructure,” inIEEE Globecom Wkshps, 2023, pp. 1039– 1044

2023

[12] [12]

Traffic-Aware Trusted Node Placement and Re- source Allocation in Multi-Band EONs Secured With QKD,

M. R. Dibajet al., “Traffic-Aware Trusted Node Placement and Re- source Allocation in Multi-Band EONs Secured With QKD,”Journal of Lightwave Tech., vol. 43, no. 1, pp. 6–18, 2025

2025

[13] [13]

Tidal-traffic-aware routing and spectrum allocation in elastic optical networks,

B. Yanet al., “Tidal-traffic-aware routing and spectrum allocation in elastic optical networks,”Journal of Optical Commun. and Netw., vol. 10, no. 11, pp. 832–842, 2018

2018

Trusted Repeater Placement in QKD-enabled Optical Networks

The reading

Core claim §

What carries the argument

Load-bearing premise §

What would settle it §

If this is right

Where Pith is reading between the lines

discussion (0)

Core claim

Load-bearing premise

What would settle it