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arxiv: 2604.24554 · v1 · submitted 2026-04-27 · 🪐 quant-ph · cs.NI

Balancing Quantum Memories in Asymmetric Repeaters for High-Fidelity Entanglement Distribution

Karim S. Elsayed , Amr Rizk This is my paper

Pith reviewed 2026-05-08 03:54 UTC · model grok-4.3

classification 🪐 quant-ph cs.NI
keywords quantum repeatersasymmetric repeatersquantum memoriesentanglement fidelitymemory allocationentanglement distributionquantum internetdecoherence
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The pith

Dynamic memory allocation in asymmetric quantum repeaters boosts entanglement fidelity at comparable rates.

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

Quantum repeaters enable long-distance entanglement but face fidelity losses in asymmetric setups where distances to neighboring nodes differ. Standard sequential memory use causes early entanglements to decohere during waits for matches on the slower side. The paper introduces a dynamic allocation of different memory counts to each side to balance generation probabilities and reduce storage times. It derives an optimal allocation strategy along with statistical lower bounds on rate and fidelity. This approach yields higher fidelity than both standard and fixed-allocation repeaters without rate loss.

Core claim

The paper establishes that in asymmetric repeaters, where link distances vary, a mismatch in generated entanglements leads to decoherence and reduced fidelity. By deriving a dynamic optimal memory allocation that assigns unequal numbers of memories to the left and right sides according to their respective generation probabilities, the mismatch is mitigated. Statistical lower bounds are then obtained for the achievable entanglement rate and fidelity under this allocation. The results show that this optimal allocation significantly enhances fidelity while maintaining a rate comparable to the standard repeater, in contrast to fixed allocations which can harm fidelity.

What carries the argument

Dynamic optimal memory allocation that balances the number of memories assigned to left and right entanglement generation according to link asymmetries.

If this is right

  • The optimal allocation yields statistical lower bounds on the achievable rate and fidelity.
  • Fidelity improves significantly compared to the standard repeater.
  • The rate stays comparable to the standard repeater.
  • Fixed memory allocation can reduce fidelity in asymmetric configurations.

Where Pith is reading between the lines

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

  • The allocation strategy could extend to chains of repeaters with multiple asymmetric links for better end-to-end performance.
  • Adaptive memory management may become necessary in real quantum networks where link distances fluctuate.
  • The bounds could guide hardware design choices for memory counts in practical deployments.

Load-bearing premise

Entanglement generation probabilities and decoherence times follow standard memory models accurately even across different distances, and dynamic allocation can be executed with negligible control overhead.

What would settle it

A simulation or experiment on an asymmetric repeater showing that the dynamic optimal allocation fails to achieve higher fidelity than the standard repeater at comparable rates would falsify the improvement.

Figures

Figures reproduced from arXiv: 2604.24554 by Amr Rizk, Karim S. Elsayed.

Figure 1
Figure 1. Figure 1: (a) System-level view: Asymmetric quantum repeater connecting two quantum nodes with different distances dl ̸= dr. Quantum nodes may be end nodes or quantum repeaters. (b) Schematic illustration of the considered repeater ar￾chitecture: The repeater contains N memories dynamically allocated between the left and right sides to form entangle￾ments with neighboring nodes. The number of memories Nl allocated t… view at source ↗
Figure 2
Figure 2. Figure 2: Schematic illustration of the standard repeater archi view at source ↗
Figure 3
Figure 3. Figure 3: Asymmetric repeater rate evaluation under differ view at source ↗
Figure 4
Figure 4. Figure 4: Asymmetric repeater fidelity evaluation under different memory allocation regimes: Optimal memory allocation (blue), view at source ↗
Figure 5
Figure 5. Figure 5: Qualitative example of an asymmetric repeater evalua view at source ↗
Figure 6
Figure 6. Figure 6: (a) Schematic illustration: A repeater chain consisting of two repeaters, R1 and R2, connecting two end nodes, Q1 and Q2. Each node, i.e., repeater or end node, contains a total number of N memories. Each repeater has the architecture considered in this work from Fig. 1b and optimally assigns memories to its sides using Lem. 1. (b) Numerical evaluation: Comparison of the expected fidelity and expected rate… view at source ↗
read the original abstract

At the core of the quantum Internet lie quantum repeaters that enable remote end-to-end entanglement generation. Fundamentally, the entanglement generation rate and fidelity of quantum repeaters constitute the bottleneck for end-to-end performance. To achieve high rates, quantum repeaters employ quantum memory multiplexing. In a high-rate standard repeater, each memory sequentially generates an entanglement with its neighboring nodes and then applies entanglement swapping. This, however, results in low fidelity due to decoherence of the first-formed entanglement in the sequential generation process. By allocating different numbers of memories to simultaneously form entanglements with the left and right adjacent nodes, quantum repeaters reduce high waiting times and achieve high fidelity. In such a repeater, a mismatch problem arises due to the difference between the probabilistic number of generated entanglements on both sides. Consequently, some entanglements remain stored until opposite entanglements are available. The mismatch problem reduces the repeater rate and particularly the entanglement fidelity. In this paper, we consider the mismatch problem in an asymmetric repeater with different distances to its adjacent nodes. To mitigate the mismatch problem, we derive a dynamic optimal memory allocation. Under the optimal allocation, we derive statistical lower bounds on the achievable rate and fidelity. We demonstrate that the optimal allocation significantly improves the fidelity while maintaining a comparable rate to the standard repeater. In contrast, our results show that fixed memory allocation may be detrimental to the fidelity.

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 paper addresses mismatch in entanglement generation for asymmetric quantum repeaters (unequal distances to left/right neighbors) by deriving a dynamic optimal memory allocation rule. Under this rule it obtains statistical lower bounds on rate and fidelity, claims significant fidelity gains over both the standard sequential repeater and any fixed allocation, while keeping rate comparable.

Significance. If the bounds are robust, the work supplies a concrete, implementable resource-balancing technique for realistic non-symmetric repeater chains, which are the norm in deployed networks. The provision of statistical lower bounds (rather than simulation-only results) is a positive feature that could support performance guarantees.

major comments (2)
  1. [§3 (System Model) and bounds derivation] §3 (System Model) and the subsequent derivation of the lower bounds: the model treats entanglement attempts as independent Bernoulli trials in synchronized discrete time slots with fixed p_L and p_R. Asymmetric distances produce unequal photon propagation delays and round-trip times, rendering generation events asynchronous; this alters the joint waiting-time distribution, storage-duration statistics, and therefore the fidelity decay that the allocation rule is intended to mitigate. The resulting lower bounds on fidelity are therefore derived under an assumption that directly contradicts the physical timing of the asymmetric setting.
  2. [Optimality derivation and performance comparison sections] The optimality proof and the comparison to fixed allocation (e.g., the claim that fixed allocation is 'detrimental to fidelity') rest on the same synchronized discrete-time mismatch statistics. Because asynchrony changes the effective mismatch process, the quantitative improvement and the statistical lower bounds cannot be taken as established without an asynchronous continuous-time analysis or a demonstration that the discrete approximation remains accurate to first order.
minor comments (2)
  1. [Abstract] The abstract states that 'optimal allocation and statistical lower bounds were derived' yet gives neither the explicit allocation rule nor the form of the bounds; a one-sentence statement of the key modeling assumptions would improve readability.
  2. [Notation and §4] Notation for left/right memory counts and success probabilities should be introduced once and used uniformly; several passages switch between p_L/p_R and p_left/p_right without redefinition.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the detailed and constructive report. The comments highlight an important modeling assumption in our work. We address each major comment below and outline revisions that will strengthen the manuscript by clarifying the scope of the results.

read point-by-point responses

  1. Referee: §3 (System Model) and the subsequent derivation of the lower bounds: the model treats entanglement attempts as independent Bernoulli trials in synchronized discrete time slots with fixed p_L and p_R. Asymmetric distances produce unequal photon propagation delays and round-trip times, rendering generation events asynchronous; this alters the joint waiting-time distribution, storage-duration statistics, and therefore the fidelity decay that the allocation rule is intended to mitigate. The resulting lower bounds on fidelity are therefore derived under an assumption that directly contradicts the physical timing of the asymmetric setting.

    Authors: We agree that the discrete-time synchronized-slot model with fixed p_L and p_R is an approximation. It is adopted because it permits closed-form statistical lower bounds on rate and fidelity while still capturing the core mismatch arising from unequal link success probabilities. In the revised manuscript we will expand §3 to explicitly state this modeling choice, derive the effective p_L and p_R from the physical distances and attempt rates, and add a paragraph discussing the conditions under which the synchronized approximation remains reasonable (e.g., when clock synchronization or buffering is employed). We will also note that a full continuous-time asynchronous analysis would require a different stochastic-process framework and is left for future work. The derived bounds and the optimality of the dynamic allocation therefore hold rigorously inside the stated discrete-time model. revision: yes

  2. Referee: The optimality proof and the comparison to fixed allocation (e.g., the claim that fixed allocation is 'detrimental to fidelity') rest on the same synchronized discrete-time mismatch statistics. Because asynchrony changes the effective mismatch process, the quantitative improvement and the statistical lower bounds cannot be taken as established without an asynchronous continuous-time analysis or a demonstration that the discrete approximation remains accurate to first order.

    Authors: The optimality derivation and the fidelity comparisons are performed under the discrete-time mismatch statistics defined in §3. We will revise the optimality section and the performance-comparison paragraphs to make this scope explicit, replace absolute claims with qualified statements such as “within the discrete-time model,” and add a short discussion of the approximation error. No numerical results will be altered, but the language will be tempered and a forward-looking remark on continuous-time extensions will be included. These changes address the referee’s concern without requiring a complete re-derivation at this stage. revision: yes

standing simulated objections not resolved
  • A complete asynchronous continuous-time analysis of the dynamic allocation rule and the resulting fidelity bounds, which would necessitate an entirely different mathematical treatment.

Circularity Check

0 steps flagged

No circularity: derivation of allocation and bounds is self-contained

full rationale

The paper models the mismatch problem in asymmetric repeaters via independent probabilistic entanglement generation on left and right sides, derives a dynamic optimal memory allocation rule to balance the resulting waiting times, and then obtains statistical lower bounds on rate and fidelity directly from the resulting joint distributions of storage durations and success events. No step reduces by construction to a fitted parameter renamed as a prediction, a self-citation chain, or an ansatz smuggled in from prior work by the same authors; the bounds are presented as consequences of the allocation rule applied to the stated probabilistic model rather than being equivalent to the inputs by definition. The derivation therefore remains independent of the target fidelity metric.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard quantum-memory models (decoherence rates, probabilistic entanglement generation) that are treated as given; no new entities are postulated and no free parameters are explicitly fitted in the abstract.

axioms (2)
  • domain assumption Entanglement generation on each side follows independent probabilistic processes whose success probabilities depend on link distance and memory quality.
    Invoked to define the mismatch problem and the optimal allocation rule.
  • domain assumption Decoherence acts as an exponential decay on stored entanglement fidelity while waiting for the opposite-side pair.
    Used to quantify the fidelity penalty of waiting times.

pith-pipeline@v0.9.0 · 5551 in / 1363 out tokens · 44219 ms · 2026-05-08T03:54:13.252106+00:00 · methodology

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