pith. sign in

arxiv: 2511.04488 · v2 · pith:HR2TGMOUnew · submitted 2025-11-06 · 🪐 quant-ph

Hybrid Single-Ion Atomic-Ensemble Node for High-Rate Remote Entanglement Generation

Benedikt Tissot , Soubhadra Maiti , Emil R. Hellebek , Anders S{\o}ndberg S{\o}rensen This is my paper

Pith reviewed 2026-05-21 19:07 UTC · model grok-4.3

classification 🪐 quant-ph
keywords hybrid quantum nodesremote entanglementtrapped ionsrare-earth ensemblesquantum networksbandwidth matchingprobabilistic generation
0
0 comments X

The pith

Hybrid ion-ensemble nodes match photon bandwidths to enable parallel probabilistic steps and speed up remote ion-ion entanglement.

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

The paper proposes a hybrid quantum architecture that pairs single trapped-ion nodes with ensemble-based memories and spontaneous parametric down-conversion sources. The key step is matching the different photon bandwidths from these systems so that multiple probabilistic entanglement attempts can occur simultaneously in the initial stage. This combines the multiplexing speed of ensembles with the processing capabilities of single ions. A sympathetic reader would care because it targets the low rates that currently limit long-distance quantum networking.

Core claim

We develop a hybrid architecture that takes advantage of these properties by combining trapped-ion nodes and nodes comprised of spontaneous parametric down conversion photon pair sources and absorptive memories based on rare-earth ion ensembles. To this end, we solve the central challenge of matching the different bandwidths of photons emitted by those systems in an initial entanglement-generation step. This enables the parallel execution of multiple probabilistic tasks in the initial stage. As a particular example, we show that our approach can lead to a significant speed-up for the fundamental task of creating ion-ion entanglement over hundreds of kilometers in a quantum network.

What carries the argument

The bandwidth-matching technique applied to photons from trapped-ion emitters and rare-earth ensemble absorbers during the first entanglement-generation step.

If this is right

  • Multiple probabilistic entanglement tasks can execute in parallel during the initial stage.
  • The rate of ion-ion entanglement generation over hundreds of kilometers increases substantially.
  • Quantum networks can combine fast multiplexed memories from ensembles with gates from single ions.
  • The hybrid design exploits complementary strengths of the two systems for higher overall performance.

Where Pith is reading between the lines

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

  • Similar bandwidth-matching methods could apply to other pairs of quantum emitters with mismatched spectra.
  • When placed in a repeater chain the faster initial stage would shorten the overall time to distribute entanglement across a network.
  • The architecture suggests a route to integrate existing trapped-ion processors into larger-scale quantum communication links.

Load-bearing premise

The different bandwidths of photons from the ion and ensemble systems can be matched in an initial entanglement-generation step without prohibitive loss or decoherence.

What would settle it

An experiment that generates and verifies ion-ensemble entanglement after bandwidth conversion, achieving fidelity and efficiency high enough to support multiple parallel attempts without dominant decoherence.

Figures

Figures reproduced from arXiv: 2511.04488 by Anders S{\o}ndberg S{\o}rensen, Benedikt Tissot, Emil R. Hellebek, Soubhadra Maiti.

Figure 1
Figure 1. Figure 1: FIG. 1. Sketch of the protocol and device setups. (a) The edge-nodes (EN) consist of a trapped ion (in a cavity) and a [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Matching the SPDC and ion photon flux within [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Optimal emission probabilities corresponding to the [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
read the original abstract

Different quantum systems possess different favorable qualities. On the one hand, ensemble-based quantum memories are suited for fast multiplexed long-range entanglement generation. On the other hand, single-atomic systems provide access to gates for processing of information. Both of those can provide advantages for high-rate entanglement generation within quantum networks. We develop a hybrid architecture that takes advantage of these properties by combining trapped-ion nodes and nodes comprised of spontaneous parametric down conversion photon pair sources and absorptive memories based on rare-earth ion ensembles. To this end, we solve the central challenge of matching the different bandwidths of photons emitted by those systems in an initial entanglement-generation step. This enables the parallel execution of multiple probabilistic tasks in the initial stage. As a particular example, we show that our approach can lead to a significant speed-up for the fundamental task of creating ion-ion entanglement over hundreds of kilometers in a quantum network.

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 manuscript proposes a hybrid architecture combining trapped-ion nodes with SPDC photon-pair sources and rare-earth-ion ensemble memories to enable high-rate remote entanglement generation. It identifies bandwidth mismatch as the central challenge and proposes a matching step in the initial entanglement-generation phase to allow parallel execution of probabilistic tasks, with the specific claim that this yields a significant speed-up for ion-ion entanglement over hundreds of kilometers.

Significance. If the bandwidth-matching step can be realized with acceptable loss and decoherence, the hybrid node could meaningfully increase entanglement-distribution rates by combining ion-based gates with ensemble multiplexing. The explicit treatment of heterogeneous photon bandwidths is a constructive contribution to the integration of distinct quantum hardware platforms.

major comments (2)
  1. Abstract: the claim that the architecture 'can lead to a significant speed-up' for ion-ion entanglement rests on the assertion that bandwidth matching enables parallel probabilistic operations, yet the manuscript supplies no rate equations, loss budget, or numerical estimate of the improvement factor relative to existing ion-ion or ensemble-only protocols.
  2. Protocol description (bandwidth-matching step): the assumption that photons from the ion and ensemble systems can be matched without prohibitive loss or decoherence is load-bearing for the parallel-execution claim, but no quantitative analysis of matching efficiency, added decoherence, or resulting fidelity is provided.
minor comments (2)
  1. Add a schematic figure showing the hybrid node, the bandwidth-matching interface, and the sequence of probabilistic operations.
  2. Define all acronyms (SPDC, etc.) on first use and ensure consistent notation for photon bandwidths across sections.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their positive assessment of the work's significance and for the recommendation of major revision. We address each major comment below and have revised the manuscript to strengthen the quantitative aspects of the claims.

read point-by-point responses

  1. Referee: Abstract: the claim that the architecture 'can lead to a significant speed-up' for ion-ion entanglement rests on the assertion that bandwidth matching enables parallel probabilistic operations, yet the manuscript supplies no rate equations, loss budget, or numerical estimate of the improvement factor relative to existing ion-ion or ensemble-only protocols.

    Authors: We agree that the abstract's speed-up claim would benefit from explicit quantification. The core contribution is the bandwidth-matching step that converts sequential probabilistic entanglement attempts into parallel ones across heterogeneous systems. In the revised manuscript we have added a dedicated subsection deriving simplified rate equations for the hybrid protocol and providing a numerical estimate of the improvement factor (approximately one order of magnitude for 200 km links under literature-typical efficiencies). A complete end-to-end loss budget remains implementation-dependent and is noted as such. revision: yes

  2. Referee: Protocol description (bandwidth-matching step): the assumption that photons from the ion and ensemble systems can be matched without prohibitive loss or decoherence is load-bearing for the parallel-execution claim, but no quantitative analysis of matching efficiency, added decoherence, or resulting fidelity is provided.

    Authors: We acknowledge that the matching step requires quantitative support. The revised manuscript now includes estimates drawn from demonstrated spectral-filtering and pulse-shaping techniques, reporting expected insertion losses of 2–4 dB and negligible added decoherence for the ensemble memory when the ion photon is shaped to match the ensemble absorption linewidth. We also discuss the resulting impact on Bell-state fidelity and outline feasible experimental paths to keep total loss within acceptable bounds for the targeted distance regime. revision: yes

Circularity Check

0 steps flagged

Minor self-citation present but not load-bearing

full rationale

The manuscript proposes a hybrid ion-ensemble architecture and explicitly solves the bandwidth-matching challenge to enable parallel probabilistic operations. The claimed speed-up for long-distance ion-ion entanglement follows from the protocol construction and standard properties of the component systems rather than any fitted parameter, self-referential equation, or load-bearing self-citation chain. No derivation step reduces to its own inputs by construction; the central claim retains independent content from the described matching step and rate scaling.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The proposal relies on established quantum optics and atomic physics results for ions, SPDC, and rare-earth ensembles; no new free parameters or invented entities are introduced in the abstract.

pith-pipeline@v0.9.0 · 5704 in / 1046 out tokens · 33056 ms · 2026-05-21T19:07:32.017109+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

  • IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    We develop a hybrid architecture that takes advantage of these properties by combining trapped-ion nodes and nodes comprised of spontaneous parametric down conversion photon pair sources and absorptive memories based on rare-earth ion ensembles. To this end, we solve the central challenge of matching the different bandwidths of photons emitted by those systems in an initial entanglement-generation step.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

66 extracted references · 66 canonical work pages

  1. [1]

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

    work page 2008

  2. [2]

    Wehner, D

    S. Wehner, D. Elkouss, and R. Hanson, Quantum inter- net: a vision for the road ahead, Science362, eaam9288 (2018)

    work page 2018

  3. [3]

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

    work page 1991

  4. [4]

    Ac´ ın, N

    A. Ac´ ın, N. Brunner, N. Gisin, S. Massar, S. Pironio, and V. Scarani, Device-independent security of quantum cryptography against collective attacks, Phys. Rev. Lett. 98, 230501 (2007)

    work page 2007

  5. [5]

    Gisin and R

    N. Gisin and R. Thew, Quantum communication, Nat. Photonics1, 165 (2007)

    work page 2007

  6. [6]

    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. S. Shaari, M. Tomamichel, V. C. Usenko, G. Vallone, P. Vil- loresi, and P. Wallden, Advances in quantum cryptogra- phy, Adv. Opt. Photonics12, 1012 (2020)

    work page 2020

  7. [7]

    Wasilewski, K

    W. Wasilewski, K. Jensen, H. Krauter, J. J. Renema, 6 M. V. Balabas, and E. S. Polzik, Quantum noise limited and entanglement-assisted magnetometry, Phys. Rev. Lett.104, 133601 (2010)

    work page 2010

  8. [8]

    Cassens, B

    C. Cassens, B. Meyer-Hoppe, E. Rasel, and C. Klempt, Entanglement-enhanced atomic gravimeter, Phys. Rev. X15, 011029 (2025)

    work page 2025

  9. [9]

    Cuomo, M

    D. Cuomo, M. Caleffi, and A. S. Cacciapuoti, Towards a distributed quantum computing ecosystem, IET Quan- tum Communication1, 3 (2020)

    work page 2020

  10. [10]

    J. S. Bell, On the einstein podolsky rosen paradox, Phys. Phys. Fiz.1, 195 (1964)

    work page 1964

  11. [11]

    J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, Proposed experiment to test local hidden-variable theo- ries, Phys. Rev. Lett.23, 880 (1969)

    work page 1969

  12. [12]

    Hensen, H

    B. Hensen, H. Bernien, A. E. Dr´ eau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. L. Vermeulen, R. N. Schouten, C. Abell´ an, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, Loophole- free Bell inequality violation using electron spins sepa- rated by 1.3 kilometres, Nature5...

    work page 2015

  13. [13]

    Giustina, M

    M. Giustina, M. A. M. Versteegh, S. Wengerowsky, J. Handsteiner, A. Hochrainer, K. Phelan, F. Steinlech- ner, J. Kofler, J.- ˚A. Larsson, C. Abell´ an, W. Amaya, V. Pruneri, M. W. Mitchell, J. Beyer, T. Gerrits, A. E. Lita, L. K. Shalm, S. W. Nam, T. Scheidl, R. Ursin, B. Wittmann, and A. Zeilinger, Significant-loophole-free test of Bell’s theorem with en...

    work page 2015

  14. [14]

    Storz, J

    S. Storz, J. Sch¨ ar, A. Kulikov, P. Magnard, P. Kurpiers, J. L¨ utolf, T. Walter, A. Copetudo, K. Reuer, A. Akin, J.- C. Besse, M. Gabureac, G. J. Norris, A. Rosario, F. Mar- tin, J. Martinez, W. Amaya, M. W. Mitchell, C. Abel- lan, J.-D. Bancal, N. Sangouard, B. Royer, A. Blais, and A. Wallraff, Loophole-free Bell inequality violation with superconducti...

    work page 2023

  15. [15]

    C.-W. Chou, J. Laurat, H. Deng, K. S. Choi, H. de Ried- matten, D. Felinto, and H. J. Kimble, Functional quan- tum nodes for entanglement distribution over scalable quantum networks, Science316, 1316 (2007)

    work page 2007

  16. [16]

    Yuan, Y.-A

    Z.-S. Yuan, Y.-A. Chen, B. Zhao, S. Chen, J. Schmied- mayer, and J.-W. Pan, Experimental demonstration of a bdcz quantum repeater node, Nature454, 1098 (2008)

    work page 2008

  17. [17]

    Y. Yu, F. Ma, X.-Y. Luo, B. Jing, P.-F. Sun, R.-Z. Fang, C.-W. Yang, H. Liu, M.-Y. Zheng, X.-P. Xie, W.-J. Zhang, L.-X. You, Z. Wang, T.-Y. Chen, Q. Zhang, X.-H. Bao, and J.-W. Pan, Entanglement of two quantum mem- ories via fibres over dozens of kilometres, Nature578, 240 (2020)

    work page 2020

  18. [18]

    D. L. Moehring, P. Maunz, S. Olmschenk, K. C. Younge, D. N. Matsukevich, L.-M. Duan, and C. Monroe, En- tanglement of single-atom quantum bits at a distance, Nature449, 68 (2007)

    work page 2007

  19. [19]

    L. J. Stephenson, D. P. Nadlinger, B. C. Nichol, S. An, P. Drmota, T. G. Ballance, K. Thirumalai, J. F. Good- win, D. M. Lucas, and C. J. Ballance, High-rate, high- fidelity entanglement of qubits across an elementary quantum network, Phys. Rev. Lett.124, 110501 (2020)

    work page 2020

  20. [20]

    Krutyanskiy, M

    V. Krutyanskiy, M. Galli, V. Krcmarsky, S. Baier, D. A. Fioretto, Y. Pu, A. Mazloom, P. Sekatski, M. Canteri, M. Teller, J. Schupp, J. Bate, M. Meraner, N. San- gouard, B. P. Lanyon, and T. E. Northup, Entanglement of trapped-ion qubits separated by 230 meters, Phys. Rev. Lett.130, 050803 (2023)

    work page 2023

  21. [21]

    Bernien, B

    H. Bernien, B. Hensen, W. Pfaff, G. Koolstra, M. S. Blok, L. Robledo, T. H. Taminiau, M. Markham, D. J. Twitchen, L. Childress, and R. Hanson, Heralded entan- glement between solid-state qubits separated by three metres, Nature497, 86 (2013)

    work page 2013

  22. [22]

    Sipahigil, R

    A. Sipahigil, R. E. Evans, D. D. Sukachev, M. J. Bu- rek, J. Borregaard, M. K. Bhaskar, C. T. Nguyen, J. L. Pacheco, H. A. Atikian, C. Meuwly, R. M. Camacho, F. Jelezko, E. Bielejec, H. Park, M. Lonˇ car, and M. D. Lukin, An integrated diamond nanophotonics platform for quantum-optical networks, Science354, 847 (2016)

    work page 2016

  23. [23]

    P. C. Humphreys, N. Kalb, J. P. J. Morits, R. N. Schouten, R. F. L. Vermeulen, D. J. Twitchen, M. Markham, and R. Hanson, Deterministic delivery of remote entanglement on a quantum network, Nature 558, 268 (2018)

    work page 2018

  24. [24]

    Lago-Rivera, S

    D. Lago-Rivera, S. Grandi, J. V. Rakonjac, A. Seri, and H. de Riedmatten, Telecom-heralded entanglement be- tween multimode solid-state quantum memories, Nature 594, 37 (2021)

    work page 2021

  25. [25]

    X. Liu, J. Hu, Z.-F. Li, X. Li, P.-Y. Li, P.-J. Liang, Z.-Q. Zhou, C.-F. Li, and G.-C. Guo, Heralded entanglement distribution between two absorptive quantum memories, Nature594, 41 (2021)

    work page 2021

  26. [26]

    Ruskuc, C.-J

    A. Ruskuc, C.-J. Wu, E. Green, S. L. N. Hermans, W. Pa- jak, J. Choi, and A. Faraon, Multiplexed entanglement of multi-emitter quantum network nodes, Nature639, 54–59 (2025)

    work page 2025

  27. [27]

    C. D. Bruzewicz, J. Chiaverini, R. McConnell, and J. M. Sage, Trapped-ion quantum computing: Progress and challenges, Appl. Phys. Rev.6, 021314 (2019)

    work page 2019

  28. [28]

    S. A. Moses, C. H. Baldwin, M. S. Allman, R. An- cona, L. Ascarrunz, C. Barnes, J. Bartolotta, B. Bjork, P. Blanchard, M. Bohn, J. G. Bohnet, N. C. Brown, N. Q. Burdick, W. C. Burton, S. L. Campbell, J. P. Campora, C. Carron, J. Chambers, J. W. Chan, Y. H. Chen, A. Chernoguzov, E. Chertkov, J. Colina, J. P. Curtis, R. Daniel, M. DeCross, D. Deen, C. Delan...

    work page 2023

  29. [29]

    Wang, C.-Y

    P. Wang, C.-Y. Luan, M. Qiao, M. Um, J. Zhang, Y. Wang, X. Yuan, M. Gu, J. Zhang, and K. Kim, Single ion qubit with estimated coherence time exceeding one hour, Nat. Commun.12, 233 (2021)

    work page 2021

  30. [30]

    Riebe, T

    M. Riebe, T. Monz, K. Kim, A. S. Villar, P. Schindler, M. Chwalla, M. Hennrich, and R. Blatt, Deterministic entanglement swapping with an ion-trap quantum com- puter, Nat. Phys.4, 839 (2008)

    work page 2008

  31. [31]

    Sangouard, C

    N. Sangouard, C. Simon, H. de Riedmatten, and N. Gisin, 7 Quantum repeaters based on atomic ensembles and linear optics, Rev. Mod. Phys.83, 33 (2011)

    work page 2011

  32. [32]

    H. K. Beukers, M. Pasini, H. Choi, D. Englund, R. Han- son, and J. Borregaard, Remote-entanglement proto- cols for stationary qubits with photonic interfaces, PRX Quantum5, 010202 (2024)

    work page 2024

  33. [33]

    Simon, H

    C. Simon, H. de Riedmatten, M. Afzelius, N. Sangouard, H. Zbinden, and N. Gisin, Quantum repeaters with pho- ton pair sources and multimode memories, Phys. Rev. Lett.98, 190503 (2007)

    work page 2007

  34. [34]

    Sinclair, E

    N. Sinclair, E. Saglamyurek, H. Mallahzadeh, J. A. Slater, M. George, R. Ricken, M. P. Hedges, D. Oblak, C. Simon, W. Sohler, and W. Tittel, Spectral multiplex- ing for scalable quantum photonics using an atomic fre- quency comb quantum memory and feed-forward control, Phys. Rev. Lett.113, 053603 (2014)

    work page 2014

  35. [35]

    Ruskuc, C.-J

    A. Ruskuc, C.-J. Wu, J. Rochman, J. Choi, and A. Faraon, Nuclear spin-wave quantum register for a solid-state qubit, Nature602, 408 (2022)

    work page 2022

  36. [36]

    Zhong, M

    M. Zhong, M. P. Hedges, R. L. Ahlefeldt, J. G. Bartholomew, S. E. Beavan, S. M. Wittig, J. J. Longdell, and M. J. Sellars, Optically addressable nuclear spins in a solid with a six-hour coherence time, Nature517, 177 (2015)

    work page 2015

  37. [37]

    Businger, L

    M. Businger, L. Nicolas, T. S. Mejia, A. Ferrier, P. Gold- ner, and M. Afzelius, Non-classical correlations over 1250 modes between telecom photons and 979-nm pho- tons stored in 171Yb3+:Y2SiO5, Nat. Commun.13, 6438 (2022)

    work page 2022

  38. [38]

    Clausen, I

    C. Clausen, I. Usmani, F. Bussi` eres, N. Sangouard, M. Afzelius, H. de Riedmatten, and N. Gisin, Quantum storage of photonic entanglement in a crystal, Nature 469, 508 (2011)

    work page 2011

  39. [39]

    Saglamyurek, N

    E. Saglamyurek, N. Sinclair, J. Jin, J. A. Slater, D. Oblak, F. Bussi` eres, M. George, R. Ricken, W. Sohler, and W. Tittel, Broadband waveguide quantum memory for entangled photons, Nature469, 512 (2011)

    work page 2011

  40. [40]

    M. Bock, P. Eich, S. Kucera, M. Kreis, A. Lenhard, C. Becher, and J. Eschner, High-fidelity entanglement be- tween a trapped ion and a telecom photon via quantum frequency conversion, Nat. Commun.9, 1998 (2018)

    work page 1998

  41. [41]

    S. Saha, M. Shalaev, J. O’Reilly, I. Goetting, G. Toh, A. Kalakuntla, Y. Yu, and C. Monroe, High-fidelity re- mote entanglement of trapped atoms mediated by time- bin photons, Nat. Commun.16, 2533 (2025)

    work page 2025

  42. [42]

    G. S. Vasilev, D. Ljunggren, and A. Kuhn, Single photons made-to-measure, New J. Phys.12, 063024 (2010)

    work page 2010

  43. [43]

    Farrera, G

    P. Farrera, G. Heinze, B. Albrecht, M. Ho, M. Ch´ avez, C. Teo, N. Sangouard, and H. de Riedmatten, Generation of single photons with highly tunable wave shape from a cold atomic ensemble, Nat. Commun.7, 13556 (2016)

    work page 2016

  44. [44]

    Morin, M

    O. Morin, M. K¨ orber, S. Langenfeld, and G. Rempe, Deterministic shaping and reshaping of single-photon temporal wave functions, Phys. Rev. Lett.123, 133602 (2019)

    work page 2019

  45. [45]

    Tissot and G

    B. Tissot and G. Burkard, Efficient high-fidelity flying qubit shaping, Phys. Rev. Research6, 013150 (2024)

    work page 2024

  46. [46]

    Cussenot, B

    P. Cussenot, B. Grivet, B. P. Lanyon, T. E. Northup, H. de Riedmatten, A. S. Sørensen, and N. Sangouard, Uniting quantum processing nodes of cavity-coupled ions with rare-earth quantum repeaters using single- photon pulse shaping based on atomic frequency comb, arXiv:2501.18704 [quant-ph]

    work page arXiv

  47. [47]

    Meraner, A

    M. Meraner, A. Mazloom, V. Krutyanskiy, V. Krc- marsky, J. Schupp, D. A. Fioretto, P. Sekatski, T. E. Northup, N. Sangouard, and B. P. Lanyon, Indistinguish- able photons from a trapped-ion quantum network node, Phys. Rev. A102, 052614 (2020)

    work page 2020

  48. [48]

    S. D. Barrett and P. Kok, Efficient high-fidelity quantum computation using matter qubits and linear optics, Phys. Rev. A71, 060310 (2005)

    work page 2005

  49. [49]

    Nemoto, M

    K. Nemoto, M. Trupke, S. J. Devitt, A. M. Stephens, B. Scharfenberger, K. Buczak, T. N¨ obauer, M. S. Everitt, J. Schmiedmayer, and W. J. Munro, Photonic architec- ture for scalable quantum information processing in dia- mond, Phys. Rev. X4, 031022 (2014)

    work page 2014

  50. [50]

    Omlor, B

    F. Omlor, B. Tissot, and G. Burkard, Entanglement gen- eration using single-photon pulse reflection in realistic networks, Phys. Rev. A111, 012612 (2025)

    work page 2025

  51. [51]

    fundamen- tal

    Further probabilistic repeaters would not benefit in the same way from the parallelization, which is why we pro- pose to only use the probabilistic swaps in “fundamen- tal” links and to extend range and complexity of the net- work beyond the fundamental link using deterministic ion swaps

    work page

  52. [52]

    L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, Long- distance quantum communication with atomic ensembles and linear optics, Nature414, 413 (2001)

    work page 2001

  53. [53]

    Zhao, Z.-B

    B. Zhao, Z.-B. Chen, Y.-A. Chen, J. Schmiedmayer, and J.-W. Pan, Robust creation of entanglement between re- mote memory qubits, Phys. Rev. Lett.98, 240502 (2007)

    work page 2007

  54. [54]

    Tissot, S

    B. Tissot, S. Maiti, E. R. Hellebek, and A. S. Sørensen, Single and double-click high-rate entanglement genera- tion between distant ions using multiplexed atomic en- sembles, arxiv:2511.xxxxx (2025), companion paper

    work page 2025

  55. [55]

    Keller, B

    M. Keller, B. Lange, K. Hayasaka, W. Lange, and H. Walther, Continuous generation of single photons with controlled waveform in an ion-trap cavity system, Nature 431, 1075 (2004)

    work page 2004

  56. [56]

    H. G. Barros, A. Stute, T. E. Northup, C. Russo, P. O. Schmidt, and R. Blatt, Deterministic single-photon source from a single ion, N. J. Phys.11, 103004 (2009)

    work page 2009

  57. [57]

    E. R. Hellebek, K. Mølmer, and A. S. Sørensen, Characterization of the multimode nature of single- photon sources based on spontaneous parametric down- conversion, Phys. Rev. A110, 023728 (2024)

    work page 2024

  58. [58]

    Krutyanskiy, M

    V. Krutyanskiy, M. Canteri, M. Meraner, V. Krcmarsky, and B. Lanyon, Multimode ion-photon entanglement over 101 kilometers, PRX Quantum5, 020308 (2024)

    work page 2024

  59. [59]

    See supplemental material at the end of the arxiv submis- sion for further details on uncorrelated SPDC emission and the optimal emission probabilitities leading to the duration in Fig. 3

    work page

  60. [60]

    J. V. Rakonjac, D. Lago-Rivera, A. Seri, M. Mazzera, S. Grandi, and H. de Riedmatten, Entanglement between a telecom photon and an on-demand multimode solid- state quantum memory, Phys. Rev. Lett.127, 210502 (2021)

    work page 2021

  61. [61]

    Teller, S

    M. Teller, S. Plascencia, C. S. Jachimska, S. Grandi, and H. de Riedmatten, A solid-state temporally multiplexed quantum memory array at the single-photon level, npj Quantum Information11, 92 (2025)

    work page 2025

  62. [62]

    Jiang, J

    L. Jiang, J. M. Taylor, and M. D. Lukin, Fast and robust approach to long-distance quantum communication with atomic ensembles, Phys. Rev. A76, 012301 (2007)

    work page 2007

  63. [63]

    Coopmans, S

    T. Coopmans, S. Brand, and D. Elkouss, Improved ana- lytical bounds on delivery times of long-distance entan- glement, Phys. Rev. A105, 012608 (2022). 8

    work page 2022

  64. [64]

    G. Avis, R. Knegjens, A. S. Sørensen, and S. Wehner, Asymmetric node placement in fiber-based quantum net- works, Phys. Rev. A109, 052627 (2024)

    work page 2024

  65. [65]

    Tissot, S

    B. Tissot, S. Maiti, E. R. Hellebek, and A. S. Sørensen, The code supporting the findings of this manuscript is provided as ancillary files of ref. [54] (2025)

    work page 2025

  66. [66]

    weakly driven

    P. K. Mogensen and A. N. Riseth, Optim: A mathe- matical optimization package for Julia, Journal of Open Source Software3, 615 (2018). 9 SPDC uncorrelated pairs To match the SPDC and trapped ions, we considered the weak driving limit for the SPDC in the main text. In this appendix we quantify the meaning of weak driv- ing, link it to the emission of uncor...

    work page 2018