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arxiv: 2605.31493 · v1 · pith:NXFMXA73new · submitted 2026-05-29 · 🪐 quant-ph · cs.NI

An efficient Progressive Swapping to the Middle distribution protocol adapted to imperfect quantum memories in quantum networks

Claire Mesny , Fabrice Guillemin , Claire Goursaud This is my paper

Pith reviewed 2026-06-28 21:50 UTC · model grok-4.3

classification 🪐 quant-ph cs.NI
keywords quantum networksentanglement distributionswapping protocolsimperfect quantum memoriesprogressive swappingquantum communication
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The pith

Progressive Swapping to the Middle raises link probability over standard Progressive Swapping while using fewer resources in networks with imperfect memories.

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

The paper presents Progressive Swapping to the Middle as a new protocol for entanglement distribution along network paths. It runs Progressive Swapping from both ends until the two processes meet at the center and perform the final swap. The design accounts for memory imperfections and the resulting drop in fidelity over time. Evaluation against parallel protocols and the original Progressive Swapping shows higher link success probability, comparable fidelity, and lower resource use.

Core claim

Progressive Swapping to the Middle combines Progressive Swapping initiated from both extremities of a path so that the two fronts meet in the middle and swap the pairs they have received; when memories are imperfect and fidelity degrades, this yields higher link probability than Progressive Swapping alone, maintains reasonable fidelity, and consumes fewer resources than parallel or standard sequential protocols.

What carries the argument

Progressive Swapping to the Middle (PSM), the mechanism that merges two Progressive Swapping processes from opposite ends of the path at a central meeting point.

If this is right

  • PSM produces higher end-to-end link probability than Progressive Swapping on the same path.
  • Fidelity stays within acceptable bounds despite memory decay.
  • Fewer intermediate entangled pairs are required than in parallel distribution schemes.
  • The protocol remains viable when memory holding times are limited.

Where Pith is reading between the lines

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

  • The meeting-in-the-middle pattern may reduce the total time entangled pairs must be stored on long paths.
  • Resource savings could become larger as path length increases.
  • The same bilateral approach might be tested on other sequential entanglement protocols.

Load-bearing premise

The modeled degradation of fidelity in imperfect memories fully captures the losses that occur when the two Progressive Swapping fronts meet and swap.

What would settle it

A direct comparison, under the same memory lifetime and decoherence parameters, that finds PSM link probability no higher than that of standard Progressive Swapping would falsify the performance claim.

Figures

Figures reproduced from arXiv: 2605.31493 by Claire Goursaud, Claire Mesny, Fabrice Guillemin.

Figure 1
Figure 1. Figure 1: Scheme for the BS distribution protocol with length lr = 4 and n = 4 generations per node be the probability for a pair to be distributed from node i to its neighbor i+ 1. The probability for one generation at each source and one swap at each node to create an end-to-end pair is (3) qBS = p lr−2 swap l Yr−1 i=1 pi for lr nodes, because of events independence. Let us consider that each generation is identic… view at source ↗
Figure 2
Figure 2. Figure 2: Scheme for the HD distribution protocol with length lr = 4 and n = 4 generations 3.2.1. Success probability. This protocol makes n generations but swaps only the minimum number of pairs in common with all nodes. Let Mn lr be the minimum com￾mon number of distributed pairs on a route of length lr. The end-to-end probability e2e|Mn lr = m follows a binomial law B(qHD, m) with (7) qHD = p lr−2 swape −(lr−2)∆(… view at source ↗
Figure 3
Figure 3. Figure 3: Scheme for the PS with route length lr = 4 and n = 4 generations [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Scheme for the progressive swapping in the middle pro￾tocol with lr = 4 nodes and n = 4 generated pairs, the chosen middle is µ = 2 4.2.1. Success probability. The success probability follows P(e2e = k) = Xn m=0 P(e2e = k| min(Gµ, Dµ) = m) × P(min(Gµ, Dµ) = m), (20) with e2e| min(Gµ, Dµ) d= B(min(Gµ, Dµ), bµe −d∆( 1 τ1 + 1 τlr ) ). Similarly to the case for HD, P(min(Gµ, Dµ) = m) = P(min(Gµ, Dµ) ≥ m) − P(m… view at source ↗
Figure 5
Figure 5. Figure 5: Link fidelity as a function of the length of the route for a distance of L = 80km between nodes, n = 30 generations, a memory life-time τ = 40ms, a time-slot of ∆ = 2ms and a swap probability of pswap = 0.9 PSM being about as efficient as HD, and even better for longer distances. It is worth noting that for better memories the HD protocol can be more efficient than all the others, especially as distances i… view at source ↗
Figure 6
Figure 6. Figure 6: Probability to establish at least one end-to-end pair as a function of the length of the route for a distance of L = 80km between nodes, n = 30 generations, a memory life-time τ = 40ms, a time-slot of ∆ = 2ms and a swap probability of pswap = 0.9 We observe an overall advantage in resource consumption for PSM in the case of short lived quantum memories and repeaters placed at less than 100km from each othe… view at source ↗
Figure 7
Figure 7. Figure 7: Minimal number n ∗ of generations per node or at the start node as a function of the length of the route [4] K. Chakraborty, D. Elkouss, B. Rijsman, and S. Wehner, “Entanglement distribution in a quantum network: A multicommodity flow-based approach,” IEEE Transactions on Quantum Engineering, vol. 1, p. 1–21, 2020. [Online]. Available: http://dx.doi.org/10.1109 /TQE.2020.3028172 [5] W. Duer, H.-J. Briegel,… view at source ↗
Figure 8
Figure 8. Figure 8: Total number of generated pairs during each protocol as a function of the length of the route for a distance of L = 80km between nodes, n = 30 generations, a memory life-time τ = 40ms, a time-slot of ∆ = 2ms and a swap probability of pswap = 0.9 [11] L. Chen, K. Xue, J. Li, R. Li, N. Yu, Q. Sun, and J. Lu, “Q-ddca: Decentralized dynamic congestion avoid routing in large-scale quantum networks,” IEEE/ACM Tr… view at source ↗
read the original abstract

The distribution of entangled pairs of photons on the links composing a quantum network, combined with Bell state measurements and teleportation, is the basic apparatus to transfer quantum bits (qubits) over long distances. Entanglement distribution establishes an end-to-end entangled pair while consuming intermediate pairs on links and holding them for a certain time period. The technical literature identifies two main kinds of protocols, parallel and sequential ones, the latter having an advantage in resource consumption over the former. In this paper, we introduce an efficient swapping protocol called Progressive Swapping to the Middle (PSM) as it combines the existing Progressive Swapping (PS) protocol from both extremities of a path that meet in the middle where the received pairs are swapped. We compare PSM with two parallel protocols and PS; in our evaluation, we take into account imperfect memories and fidelity degradation. We demonstrate that PSM yields a much better link probability than PS while keeping a reasonable link fidelity, and shows an advantage in resource consumption over other protocols.

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 / 0 minor

Summary. The manuscript introduces the Progressive Swapping to the Middle (PSM) protocol for entanglement distribution over paths in quantum networks. PSM performs progressive swapping from both path extremities, with the resulting pairs meeting and being swapped in the middle. The work compares PSM against two parallel protocols and the existing Progressive Swapping (PS) protocol while modeling imperfect memories and fidelity degradation over time. The central claim is that PSM achieves substantially higher link probability than PS at acceptable fidelity and consumes fewer resources than the parallel alternatives.

Significance. If the quantitative evaluation holds, PSM would constitute a practical improvement for entanglement distribution under realistic memory decoherence, offering a middle ground between the resource efficiency of sequential protocols and the speed of parallel ones. The explicit treatment of imperfect memories is a strength relative to idealized models common in the literature.

major comments (2)
  1. [Abstract] Abstract: the claims that PSM 'yields a much better link probability than PS' and 'shows an advantage in resource consumption over other protocols' are asserted without any numerical results, simulation parameters, memory decoherence model, fidelity equations, or comparison tables. Because the central performance advantage is the paper's main contribution, the absence of supporting data or derivations in the supplied text renders the claim unverifiable.
  2. [Abstract] The protocol description implicitly assumes that the meeting-in-the-middle swap does not introduce additional fidelity loss or synchronization overhead beyond the modeled memory decay; no analysis or bound is supplied to justify this assumption, which is load-bearing for the fidelity claim.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. We address each major comment below and indicate the revisions planned.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claims that PSM 'yields a much better link probability than PS' and 'shows an advantage in resource consumption over other protocols' are asserted without any numerical results, simulation parameters, memory decoherence model, fidelity equations, or comparison tables. Because the central performance advantage is the paper's main contribution, the absence of supporting data or derivations in the supplied text renders the claim unverifiable.

    Authors: The abstract summarizes results whose supporting details (numerical link probabilities, resource comparisons, simulation parameters, decoherence model, fidelity equations, and tables) appear in the evaluation sections of the full manuscript. To improve direct verifiability from the abstract itself, we will add brief quantitative highlights of the observed improvements. revision: partial

  2. Referee: [Abstract] The protocol description implicitly assumes that the meeting-in-the-middle swap does not introduce additional fidelity loss or synchronization overhead beyond the modeled memory decay; no analysis or bound is supplied to justify this assumption, which is load-bearing for the fidelity claim.

    Authors: We agree that the assumption requires explicit support. In the revision we will insert a short analysis or bound quantifying the additional fidelity impact and synchronization considerations of the middle swap, showing that they remain within the modeled memory decay under the protocol parameters. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The provided abstract and context contain no equations, derivations, fitted parameters, or self-citations that could reduce a claimed result to its inputs by construction. The paper introduces a protocol (PSM) and reports comparative performance from evaluation under modeled imperfect memories; these are empirical simulation outcomes rather than first-principles predictions that loop back to definitions or prior self-citations. No load-bearing steps of the enumerated kinds are identifiable from the given text, satisfying the requirement to quote specific reductions before flagging circularity. The work is therefore self-contained at the level of protocol description and benchmarking.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The abstract provides no details on parameters, axioms, or new entities; review is limited to high-level claims.

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Reference graph

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