Quality of Service in aggregated quantum networks

Kae Nemoto; Nicol\`o Lo Piparo; William J. Munro

REVIEW 3 major objections 4 minor 49 references

Quality of Service in aggregated quantum networks

T0 review · 3 major / 4 minor · reviewed 2026-08-09 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read This paper claims that in aggregated quantum networks, fidelity cannot be optimized independently of quantum-memory lifetimes, and that quantum error correction can decrease end-to-end fidelity when path losses and coherence times are…

desk verdict A sensible QoS framework for aggregated quantum networks whose quantitative claims are currently non-reproducible because the fidelity formulas are imported and the T2-to-pd mapping is missing. read the letter →

arxiv 2501.18846 v2 pith:U2YGI26S submitted 2025-01-31 quant-ph

Nicolò Lo Piparo , William J. Munro , Kae Nemoto This is my paper · ORCID

classification quant-ph PACS 03.67.Hk03.67.Pp

keywords quantumnetworksqualityofserviceaggregatedroutingerrorcorrectionReed-Solomoncodefidelitymemorycoherence

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 introduces a Quality-of-Service (QoS) view of aggregated quantum networks, in which two remote nodes are connected by several parallel paths of different lengths and a router decides how many qudits each user sends along each path. The central claim is that the best channel assignment cannot be decided from path transmission probabilities alone: the coherence time of the receiver's quantum memories must enter the routing decision, because qudits arriving on faster paths wait in memory until the slower paths arrive. The paper also claims that quantum error correction does not always improve fidelity; for a quantum Reed-Solomon code in a two-path example, the higher-dimensional encoding wins only when the longer path's transmission probability is high enough, and below that threshold the redundancy is outweighed by loss and decoherence. These claims matter because routing protocols for near-term quantum repeater networks will need to balance fidelity, throughput, and memory usage, and the paper identifies concrete thresholds in coherence-time versus transmission-probability space where the optimal assignment changes.

What carries the argument

The central object is an aggregated path: a set of parallel links of different lengths connecting sender and receiver, with each quantum packet split into qudits distributed over the paths. The argument runs on a family of fidelity formulas F_{i+j}, quoted from the authors' companion paper on quantum aggregation with temporal delay, in which i qudits travel the shorter path and j the longer; these combine per-channel transmission probabilities p1 and p2 with a depolarization probability that represents decoherence in the receiver's quantum memories. The quantum Reed-Solomon code is the error-correcting structure that lets the receiver decode even when some qudits are lost, and the router's time-slotted assignment protocol is the decision mechanism that compares the F_{i+j} values across assignments. What carries the argument is the comparison of these fidelity expressions: crossings between curves, and their dependence on coherence time through the memory-error probability, are what define the greedy, restricted, and balanced routing regimes.

What would settle it

Re-derive the fidelity expressions from the companion paper with an explicit T2-to-memory-error model and evaluate the 5+2 versus 5+0 crossover at p1 equals 0.9: the paper predicts 5+2 wins only for p2 above about 0.75 and only for sufficiently large T2. A simulation or experiment that measures end-to-end fidelity for the ten-channel, two-path setup in the T2 interval from 0.1 to 1 ms would confirm or overturn that ordering; if the ordering of configurations varies with the assumed memory model, the central routing rule is not robust.

Watch

Extended reading notes

Core claim

On its own terms, the paper's discovery is that end-to-end fidelity in an aggregated quantum network is a joint function of per-path transmission probabilities and of how long states wait in imperfect quantum memories. For unencoded transmission, the fidelity of each assignment is computed from expressions such as F_{i+j} in which i qudits travel the shorter path and j the longer, and the paper shows that finite coherence time can reorder which assignment gives the highest fidelity. For encoded transmission, the discovery is sharper: using a quantum Reed-Solomon code of larger dimension can lower fidelity. In the worked example, configuration 5+2 (a seven-dimensional code split across paths) only beats 5+0 (a five-dimensional code entirely on the good path) for transmission probability p2 greater than about 0.75, and this crossover shifts to higher p2 as the memory coherence time T2 decreases; below about 1 ms the coherence time materially changes the optimal choice, and below about 0.2 ms the fair restricted-regime assignment also changes. The authors conclude that a quantum router must know the remote memory coherence time to make correct assignments.

Load-bearing premise

The numerical thresholds rest on the fidelity formulas from the authors' companion paper, quoted in Appendix A without derivation and with apparent typographical slips, and on a conversion from memory coherence time T2 to the memory error probability that the paper never specifies; if the derivation or the conversion is wrong, the optimal-assignment thresholds shift.

Editorial extensions

If this is right

A quantum router that ignores the receiver's memory coherence time will mis-rank assignments whenever T2 is below the crossing time, so QoS routing tables must include memory hardware parameters.
Below a coherence-time threshold the router should send all qudits along the best path instead of aggregating, because waiting for the slower path destroys more fidelity than the extra loss would.
Quantum error correction should be applied conditionally: in the example, the lower-dimensional code over the good path beats the higher-dimensional code split across paths when p2 is low, and only above a threshold does the larger code win.
The optimal assignment for the restricted regime, which minimizes the fidelity difference between users, changes at specific p2 values, and finite coherence time shifts those boundaries.
Current quantum memory technologies with coherence times above the identified thresholds are, according to the paper, adequate to support the proposed QoS-aware assignments.

Reading between the lines

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

Editorial inference: the crossing diagrams in T2-versus-p2 space could be turned into a simple admission-control policy, where the router uses the fidelity formulas to decide whether a requested user count and fidelity target can be met at all.
Editorial inference: the same QoS logic could be tested as a hybrid coding strategy that switches between unencoded, lower-dimensional, and higher-dimensional encodings based on live estimates of path loss and remaining memory coherence time.
Editorial inference: the paper's direct-transmission assumption leaves open whether the qualitative conclusion, that memory lifetime must enter routing decisions, survives in entanglement-based repeater networks, where stored Bell pairs face analogous decoherence but different fidelity formulas.

Share X Bluesky LinkedIn Reddit HN

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 version: this is a useful conceptual framework for QoS in direct-transmission aggregated quantum networks, with a clean three-regime taxonomy for channel assignment. The quantitative results, however, rest on fidelity formulas imported from your prior paper [35] without derivation, and the paper never specifies how T2 maps to the depolarizing probability pd used in those formulas. That makes the T2-dependent insets and thresholds (0.1 ms, 1 ms) non-reproducible from the paper alone.

What's genuinely new: the aggregation framework with greedy/balanced/restricted assignment regimes is a sensible extension of classical QoS thinking to quantum direct transmission, and the observation that QEC can hurt when path asymmetries and finite coherence combine is a useful caution for protocol designers. The paper is also honest about its simplifying assumptions (jitter ignored, no explicit fidelity threshold, topologies chosen for illustration). The qualitative radar chart comparison of application requirements is suggestive, though explicitly not data-driven.

The soft spots are real. Appendix A lists the fidelity expressions with what look like typographical dropouts (p4/74, p/7) that should be pd^4/7^4 and pd/7 in context. More importantly, there is no equation connecting T2 to pd. The insets in Figs. 4, 6, and 7 all hinge on that relationship, and without it the claimed coherence-time thresholds and the conclusion that QEC advantage appears only above p2>0.75 cannot be checked. The general statements in the abstract—that fidelity cannot be optimized independently of memory lifetimes and that QEC sometimes degrades performance—are demonstrated only for a single two-path, ten-channel example. They may well hold more broadly, but this paper doesn't prove that.

The right audience is researchers designing near-term quantum routing protocols, especially those interested in direct-transmission (non-repeater) architectures. It's a serious referee candidate: the framework is worth engaging with, and the gaps are fixable rather than fatal. I'd send it to review, but the authors must add the pd(T2) mapping and clean up the typos before the numbers can be trusted.

Referee Report

3 major / 4 minor

Summary. This manuscript extends the classical notion of Quality of Service (QoS) to aggregated quantum networks, defining quantum-specific QoS metrics (bandwidth, loss, delay, jitter) and proposing a router protocol that assigns channels to multiple users according to three regimes (greedy, balanced, restricted). The analysis covers both unencoded transmission and quantum Reed-Solomon encoded transmission over two paths of different lengths, with the central claim that optimal channel assignment depends jointly on path transmission probability and quantum memory coherence time, and that quantum error correction does not always improve fidelity. The quantitative results are based on fidelity formulas listed in Appendix A, which are taken from the authors' prior work (Ref. [35]).

Significance. If the central results are sound, the paper makes a useful step toward QoS-aware quantum routing in near-term networks, and the prediction that QEC can be detrimental under short coherence times or unbalanced path lengths is concrete and falsifiable. The paper is clearly written and the example-based development of the three routing regimes is intuitive. Credit is due for the explicit goal of connecting routing decisions to physical memory parameters, a connection often omitted in protocol-level studies. However, the load-bearing quantitative claims are not derived in this manuscript: they reduce to fidelity formulas quoted from the authors' own prior paper, and the relationship between T2 and the depolarization probability p_d is not specified, which limits reproducibility.

major comments (3)

[Appendix A] The fidelity formulas F_{4+1}, F_{3+2}, F_{2+3}, and F_{1+4} are quoted without derivation, and the printed expressions contain typographical errors: "p4/74" in F_{4+1} should presumably be p_d^4/7^4, and "p/7" in F_{1+4} should presumably be p_d/7. Since the crossings in Fig. 6, the p2 > 0.75 threshold in Fig. 7, and the coherence-time thresholds T†2 = 0.1 ms and T2 = 1 ms are all computed from these formulas, the manuscript must either derive them in the appendix or state precisely that they are taken from Ref. [35] and provide the corrected expressions verbatim.
[Secs. IV-V] The depolarization probability p_d entering the Appendix A formulas is never related to the memory coherence time T2 and the storage interval induced by the path-delay difference. The insets of Figs. 4, 6, and 7 plot fidelity versus T2 or characterize T2 thresholds, so without an explicit mapping p_d(T2, Δτ) the results cannot be reproduced from this paper alone. Because the central claim is that the optimal channel assignment depends jointly on p2 and T2, this missing mapping is load-bearing and must be supplied.
[Sec. IV] The statement "the regimes defined above are not affected by finite coherence times" is in tension with the inset of Fig. 4, where all configurations cross the 0+5 curve at T†2 = 0.1 ms, and with the text that for T2 < T†2 "the aggregation scenario is not convenient." Please clarify whether the regime definitions are unaffected or whether the optimal assignment itself changes below T†2.

minor comments (4)

[Tables I and II] The relationship between Nc = 10, a channel capacity of one qudit of dimension 9 per time unit, the qudit dimensions 7 and 3, and the resulting numbers of qudits per assignment is not derived; a short worked example would improve readability.
[Appendix A] Equation (A3) uses parentheses inconsistently with (A2); please unify the notation for the binomial-type expansions.
[Fig. 2 caption] The radar chart is described in the text as qualitative, but the caption should explicitly state that the normalized values are illustrative only and not drawn from experimental data.
[Appendix A] The manuscript cites its own Ref. [35] for the aggregation fidelity formulas; the text should make clear at the point of use in Appendix A that the expressions are imported from that work, rather than appearing to be original to this paper.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular reduction: the quantitative results are applications of previously published fidelity formulas, not restatements of the paper's own inputs.

full rationale

The paper's numerical conclusions, including the fidelity curves, the regime boundaries in Figs. 4-7, and the coherence-time thresholds, are computed from the analytical fidelity expressions listed in Appendix A and attributed to the authors' prior work, Ref. [35]. This is a genuine self-citation and it creates a reproducibility concern: Appendix A lists the expressions without derivation, and the main text never specifies how the memory coherence time T2 is converted into the depolarizing probability pd used in those formulas. However, importing a previously derived model is not circular under the review criteria. The routing assignments, regime classifications, and threshold comparisons are new consequences drawn from that model; no parameter is fitted to the quantities being predicted, and no conclusion is defined in terms of its own output. The apparent typographical issues in the formulas and the missing T2-to-pd mapping are correctness or completeness concerns, not evidence that a prediction is equivalent to its inputs by construction. Therefore no specific circular step can be exhibited, and the circularity score is zero.

Assumptions & free parameters 1 free parameters · 4 assumptions · 0 invented entities

The paper introduces no new physical entities; its building blocks are QoS concepts adapted from classical networking and fidelity formulas imported from the authors' prior work. The main unstated elements are the depolarization probability pd and its relationship to T2, along with the assumptions of negligible jitter and perfect router knowledge.

free parameters (1)

pd (depolarization probability per qudit in storage)
Used in all fidelity formulas in Appendix A and in the insets via T2, but the paper does not state its functional dependence on coherence time T2 or storage duration, so it functions as an adjustable parameter in the examples.

assumptions (4)

domain assumption End-to-end fidelity for each i+j configuration is given by the analytical formulas in Appendix A (from Ref. [35]).
All quantitative curves (Figs. 4-7) are computed from these formulas, which are quoted without derivation in this paper.
domain assumption Jitter is negligible (Sec. II).
The model assumes arrival-time differences are zero; non-zero jitter would add memory storage and decoherence effects not captured here.
domain assumption Quantum memories depolarize the stored qudits with a single error probability pd; no other decoherence mechanism is modeled.
The fidelity expressions only include a single depolarization parameter pd, ignoring amplitude damping, correlated errors, and other physical noise.
domain assumption The router has perfect knowledge of path delays, channel transmission probabilities, memory coherence times, and user requests (Sec. III).
The protocol assumes exact knowledge; estimation errors and their impact on routing decisions are not analyzed.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Quality of Service in aggregated quantum networks." pith.science (2026). https://pith.science/paper/U2YGI26S

@misc{pith2026250118846,
  author       = {Pith},
  title        = {Pith review of: Quality of Service in aggregated quantum networks},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/U2YGI26S}},
  note         = {Machine review of arXiv:2501.18846}
}

read the original abstract

Future quantum networks will enable the interconnection of multiple users distributed across vast geographic distances. Due to these large separations and limited physical resources, communication will often rely on multi-path routing strategies, where physical resources are distributed across channels of varying lengths and delivered to end users. Efficient long-distance quantum communication therefore requires optimizing the allocation of these resources across available paths. In this work, we introduce a performance-oriented approach to quantum network routing by extending the classical concept of Quality of Service (QoS) to the context of multi-path quantum resources distribution. Unlike prior models that consider entanglement generation or quantum memory coherence in isolation, we investigate the interplay between path assignment strategies, coherence time constraints, and quantum error correction (QEC), and how they jointly impact end-to-end communication fidelity. We analyze both unencoded and encoded transmissions over aggregated network paths, quantifying the effects of resource allocation on transmission success. Our findings show that fidelity cannot be optimized independently of memory lifetimes, and that while QEC can enhance performance under specific conditions, it also imposes additional constraints depending on network topology and path-length asymmetries. This work provides a foundation for developing QoS-aware quantum routing protocols that balance fidelity, throughput, and memory utilization -- key considerations for near-term quantum repeater networks.

Figures

Figures reproduced from arXiv: 2501.18846 by the authors.

**Figure 2.** The chart provides a qualitative comparison of the [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Schematic illustration of a wide-area quantum network (WAN) with quantum routers. Two local area networks (LANs), labeled “S” (source) and “R” (receiver), are connected via three distinct paths: a solid line (path 1), dashed lines (path 2), and dash-dotted lines (path 3). These paths differ in length and may each contain an arbitrary number of quantum channels, over which information can be transmitted from LAN S… view at source ↗

Figures from the paper (3 more)

**Figure 4.** Figure 4: Fidelities of the received packets at the receiver [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]

**Figure 6.** Figure 6: Absolute value of the difference between the fidelities of the transmitted states, where i, j, k and l correspond to the following configurations: 3+4 and 2+1 (red curve), 3+2 and 2+3 (blue curve), and 2+5 and 3+0 (black curve). In the restricted regime, the router as…

**Figure 7.** Figure 7: Fidelity of the transmitted state corresponding to [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

49 extracted references · 37 canonical work pages

[35]

Azuma, K

K. Azuma, K. Tamaki, and H. K. Lo, All-photonic quan- tum repeaters, Nat. Commun.6, 6787 (2015)

work page 2015
[1]

Kozlowski and S

W. Kozlowski and S. Wehner, Towards large-scale quan- tum networks, In Proceedings of the 6th ACM Interna- tional Conference on Nanoscale Computing and Commu- nication (2019)

work page 2019
[2]

low”, “medium

In a conventional quantum key distribution (QKD) Figure 2. The chart provides a qualitative comparison of the performance requirements of various applications across key QoS metrics. The normalized values are not drawn from ex- perimental data but are instead intended to illustrate con- ceptual differences among protocols, helping guide the design of rout...

work page
[3]

M. S. Blok, N. Kalb, A. Reiserer, T. H. Taminiau, and R. Hanson, Towards quantum networks of single spins: analysis of a quantum memory with an optical interface in diamond, Faraday Discuss.184, 173 (2015)

2015
[4]

Childress and R

L. Childress and R. Hanson, Diamond nv centers for quantum computing and quantum networks, MRS Bul- letin 38, 134 (2013)

work page 2013
[5]

Arute, K

F. Arute, K. Arya, R. Babbush, D. Bacon, J. C. Bardin, R. Barends, R. Biswas, S. Boixo, F. G. S. L. Brandao, D. A. Buell, B. Burkett, Y. Chen, Z. Chen, B. Chiaro, R. Collins, W. Courtney, A. Dunsworth, E. Farhi, B. Foxen, A. Fowler, C. Gidney, M. Giustina, R. Graff, K.Guerin, S.Habegger, M.P.Harrigan, M.J.Hartmann, A. Ho, M. Hoffmann, T. Huang, T. S. Humb...

work page 2019
[6]

H. J. Kimble, The quantum internet, Nature453, 1023 (2008)

2008
[7]

Nielsen and I

M. Nielsen and I. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000)

2000

Show all 49 references

[8]

W. J. Munro, K. Azuma, K. Tamaki, and K. Nemoto, In- side quantum repeaters, IEEE Journal of Selected Topics in Quantum Electronics21, 6400813 (2015)

2015
[9]

Raussendorf and H

R. Raussendorf and H. J. Briegel, A one-way quantum computer, Phys. Rev. Lett.86, 5188 (2001)

2001
[10]

Bennett and D

C. Bennett and D. DiVincenzo, Quantum information and computation, Nature404, 247 (2000)

2000
[11]

Duan and R

L.-M. Duan and R. Raussendorf, Scalable photonic quan- tum computation through cavity-assisted interactions, Phys. Rev. Lett.95, 080503 (2005)

2005
[12]

Knill, Quantum computing with realistically noisy de- vices, Nature434, 39 (2005)

E. Knill, Quantum computing with realistically noisy de- vices, Nature434, 39 (2005)

2005
[13]

A. K. Ekert, Quantum cryptography based on bell’s the- orem, Phys. Rev. Lett.67, 661 (1991)

1991
[14]

Hwang, Quantum key distribution with high loss: Toward global secure communication, Phys

W.-Y. Hwang, Quantum key distribution with high loss: Toward global secure communication, Phys. Rev. Lett. 91, 057901 (2003)

2003
[15]

Bunandar, A

D. Bunandar, A. Lentine, C. Lee, H. Cai, C. M. Long, N. Boynton, N. Martinez, C. DeRose, C. Chen, M. Grein, D. Trotter, A. Starbuck, A. Pomerene, S. Hamilton, F. N. C. Wong, R. Camacho, P. Davids, J. Urayama, and D. Englund, Metropolitan quantum key distribution with silicon p...

2018
[16]

Qiu, Quantum communications leap out of the lab, Nature 508, 441 (2014)

J. Qiu, Quantum communications leap out of the lab, Nature 508, 441 (2014)

2014
[17]

L. A. Lugiato, A. Gatti, and E. Brambilla, Quantum imaging, J. Opt. B4, 176 (2002)

2002
[18]

D. S. Simon, G. Jaeger, and A. V. Sergienko, Quan- tum metrology, imaging, and communication book, Int. J. Quantum Inform.12, 1430004 (2014)

2014
[19]

Fanizza, F

M. Fanizza, F. Kianvash, and V. Giovannetti, Quantum flags and new bounds on the quantum capacity of the de- polarizing channel, Phys. Rev. Lett.125, 020503 (2020)

2020
[20]

C. L. Dogen, F. Reinhard, and P. Cappellaro, Quantum sensing, Rev. Mod. Phys.89, 035002 (2017)

2017
[21]

M. E. Shirokov, Uniform continuity bounds for character- istics of multipartite quantum systems, Journal of Math- ematical Physics58, 102202 (2017)

2017
[22]

Rosati, A

M. Rosati, A. Mari, and V. Giovannetti, Narrow bounds for the quantum capacity of thermal attenuators, Nat. Commun. 9, 4339 (2018)

2018
[23]

explored how trade-offs between fidelity, latency, and throughput arise in realistic quantum architectures. Their work showed that multipath transmission can en- hance network resource utilization, motivating our in- vestigation of aggregated quantum networks (AQNs), in which ...

2025 arXiv
[24]

Skrzypczyk and S

M. Skrzypczyk and S. Wehner, An architecture for meet- ing quality-of-service requirements in multi-user quan- tum networks, arXiv:2111.13124 (2021)

2021 arXiv
[25]

C.Cicconetti, M.Conti,andA.Passarella,Qualityofser- vice in quantum networks, IEEE Network36, 24 (2022)

2022
[26]

W. J. Munro, A. M. Stephens, S. J. Devitt, K. A. Harri- son, and K. Nemoto, Quantum communication without the necessity of quantum memories, Nature Photonics6, 777 (2012)

2012
[27]

Abana, M

A. Abana, M. Cubeddu, V. S. Man, and A. Battou, En- tanglement routing in quantum networks: A comprehen- sive survey, arXiv:2408.01234 (2024)

2024 arXiv
[28]

J. Li, M. Wang, Q. jia, K. Sue, N. Yu, Q. Sun, and J. Lu, Fidelity-guarantee entanglement routing in quantum net- works, arXiv:2111.07764v4 (2022)

2022 arXiv
[29]

K. Li, V. Chaudhary, S. Sanchez Garcia, and K. R. Chowdhury, Q-firm: Fidelity-based rate maximizing routes for quantum networks, (2023)

2023
[30]

T. C. Ralph, A. J. F. Hayes, and A. Gilchrist, Loss- tolerant optical qubits, Phys. Rev. Lett. 95, 100501 (2005)

2005
[31]

A. G. Fowler, D. S. Wang, C. D. Hill, T. D. Ladd, R. Van Meter, and L. C. L. Hollenberg, Surface code quantum communication, Phys. Rev. Lett.104, 180503 (2010)

2010
[32]

Jiang, J

L. Jiang, J. M. Taylor, K. Nemoto, W. J. Munro, R. Van Meter, and M. D. Lukin, Quantum repeater with encoding, Phys. Rev. A , 032325 (2009)

2009
[33]

Gottesman, A

D. Gottesman, A. Kitaev, and J. Preskill, Encoding a qubit in an oscillator, Phys. Rev. A64, 012310 (2001)

2001
[34]

A. G. Fowler, D. S. Wang, C. H. Hill, T. D. Ladd, R. Van Meter, and C. L. Hollenberg, Surface code quantum communication, Phys. Rev. Lett.104, 180503 (2010)

2010
[36]

Mulidharan, J

S. Mulidharan, J. Kim, N. Lutkenhaus, M. D. Lucian, and L. Jiang, Ultrafast and fault-tolerant quantum com- munication across long distances, Phys. Rev. Lett.112, 250501 (2014)

2014
[37]

Lo Piparo, W

N. Lo Piparo, W. J. Munro, and K. Nemoto, Quan- tum aggregation with temporal delay, Phys. Rev. A110, 032613 (2024)

2024
[38]

Accordingly, we refine the definition of de- lay for such paths

Based on these observations, we generalize an aggregated path as a set of paths connecting two nodes with vary- 11 ing delays. Accordingly, we refine the definition of de- lay for such paths. For intuition, assume temporal delays are negligible, so delay depends only on path l...
[39]

Bunandar, A

D. Bunandar, A. Lentine, C. Lee, H. Cai, C. M. Long, N. Boynton, N. Martinez, C. DeRose, C. Chen, M. Grein, A. Trotter, A. Starbuck, A. Pomerene, S. Hamilton, F. N. C. Wong, R. Camacho, P. Davids, J. Urayama, and D. Englund, Metropolitan quantum key distribution with silicon p...

2018
[40]

S. J. Devitt, A. M. Stephens, W. J. Munro, and K. Nemoto, Requirements for fault-tolerant factoring on an atom-optics quantum computer, Nature Communica- tions 4, 2524 (2013)

2013
[41]

Panayi, M

C. Panayi, M. Razavi, X. Ma, and N. Lutken- haus, Memory-assisted measurement-device-independent quantum key distribution, New J. Phys. 16, 043005 (2014)

2014
[42]

S. Zhou, M. Zhang, J. Preskill, and L. Jiang, Achieving the heisenberg limit in quantum metrology using quan- tum error correction, Nat. Commun.9, 78 (2018)

2018
[43]

S. Zhou, M. Zhang, J. Preskill, and L. Jiang, Achiev- ing the heisenberg limit in quantum metrology using quantum error correction, Nature Communications9, 78 (2018)

2018
[44]

Elliott, Building the quantum network, New J

C. Elliott, Building the quantum network, New J. Phys. 4, 46 (2002)

2002
[45]

Korzh, C

B. Korzh, C. W. Lim, R. Houlmann, N. Gisin, L. M. J., D. Nolan, S. B., R. Thew, and Z. H., Provably secure and practical quantum key distribution over 307 km of optical fiber, Nature Photonics9, 163 (2015)

2015
[46]

Van Meter and D

R. Van Meter and D. Horsman, A blueprint for building a quantum computer, Communications of the ACM10, 83 (2013)

2013
[47]

Grassl, W

M. Grassl, W. Geiselmann, and T. Beth, Loss-tolerant optical qubits, International Symposium on Applied Algebra, Algebraic Algorithms, and Error-Correcting Codes, , 231 (1999)

1999
[48]

I. F. Akyildiz, X. Wang, and W. Wang, Wireless mesh networks: A survey, Computer Networks47, 445 (2005)

2005
[49]

Liu and M

K. Liu and M. El Zarki, Qos routing in wireless ad hoc networks, IEEE Network19(3), 12 (2005). Appendix A: Fidelities used in the unencoded case Here we list the analytical expressions for the fidelities used to determine the curves in Fig. 4. We denote with Fi+j the fidelity ...

2005

Pith tools

Reviewed August 9, 2026 · model on record in the stance chip above.

[1] [35]

Azuma, K

K. Azuma, K. Tamaki, and H. K. Lo, All-photonic quan- tum repeaters, Nat. Commun.6, 6787 (2015)

work page 2015

[2] [1]

Kozlowski and S

W. Kozlowski and S. Wehner, Towards large-scale quan- tum networks, In Proceedings of the 6th ACM Interna- tional Conference on Nanoscale Computing and Commu- nication (2019)

work page 2019

[3] [2]

low”, “medium

In a conventional quantum key distribution (QKD) Figure 2. The chart provides a qualitative comparison of the performance requirements of various applications across key QoS metrics. The normalized values are not drawn from ex- perimental data but are instead intended to illustrate con- ceptual differences among protocols, helping guide the design of rout...

work page

[4] [3]

M. S. Blok, N. Kalb, A. Reiserer, T. H. Taminiau, and R. Hanson, Towards quantum networks of single spins: analysis of a quantum memory with an optical interface in diamond, Faraday Discuss.184, 173 (2015)

2015

[5] [4]

Childress and R

L. Childress and R. Hanson, Diamond nv centers for quantum computing and quantum networks, MRS Bul- letin 38, 134 (2013)

work page 2013

[6] [5]

Arute, K

F. Arute, K. Arya, R. Babbush, D. Bacon, J. C. Bardin, R. Barends, R. Biswas, S. Boixo, F. G. S. L. Brandao, D. A. Buell, B. Burkett, Y. Chen, Z. Chen, B. Chiaro, R. Collins, W. Courtney, A. Dunsworth, E. Farhi, B. Foxen, A. Fowler, C. Gidney, M. Giustina, R. Graff, K.Guerin, S.Habegger, M.P.Harrigan, M.J.Hartmann, A. Ho, M. Hoffmann, T. Huang, T. S. Humb...

work page 2019

[7] [6]

H. J. Kimble, The quantum internet, Nature453, 1023 (2008)

2008

[8] [7]

Nielsen and I

M. Nielsen and I. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000)

2000