arxiv: 2604.05321 · v1 · submitted 2026-04-07 · 🪐 quant-ph

Addressing a device in a quantum network: A quantum approach including routing

Alexander Pirker This is my paper

Pith reviewed 2026-05-10 20:10 UTC · model grok-4.3

classification 🪐 quant-ph

keywords quantum networksquantum addressingentanglementquantum routingcontrolled teleportationsuperposition

0 comments p. Extension

The pith

Devices in a quantum network can be addressed using quantum states instead of classical messages, enabling tasks in superposition.

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

The paper introduces a quantum addressing scheme for networks in which devices hold quantum address states that are combined with request states encoding desired tasks. This method eliminates the need to send addresses or operation instructions classically. By leveraging entanglement, the scheme supports applications such as overlaying multiple network states. A distributed routing protocol is presented that uses Bell-state entanglement to coherently choose routes for controlled teleportation. The work concludes by proving that this quantum addressing approach is equivalent to performing tasks in superposition throughout the quantum network.

Core claim

In this work we propose an addressing scheme for quantum networks which relies on quantum states held by devices. Quantum network devices use their address state together with a request state that encodes the tasks to be executed. Our approach not only removes the necessity to classically communicate addresses, but also the need to communicate the operations a device must apply. It turns out that utilizing entanglement to encode addresses of devices in a quantum network leads to interesting applications such as overlaying different network states. We present a distributed quantum routing protocol using entanglement that coherently selects a route in a network of Bell-states for controlled-

What carries the argument

Quantum address states combined with request states, together with entanglement-based routing using Bell states for coherent route selection and controlled teleportation.

Load-bearing premise

The scheme assumes that quantum devices can prepare, store, and manipulate entangled address and request states while maintaining coherence and entanglement across the network.

What would settle it

An experiment in which quantum address states are prepared and used for routing but the expected superposition of tasks fails to occur, or where classical communication remains necessary to complete the operations.

Figures

Figures reproduced from arXiv: 2604.05321 by Alexander Pirker.

**Figure 2.** Figure 2: A quantum network and its associated spanning tree for routing from the perspective of device 1. For illustration, consider the network shown in [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Figure 3: A network of eight devices, where channels represent [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗

read the original abstract

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.

Desk Editor's Note private letter to a colleague

The paper offers a quantum addressing protocol that drops classical control messages via entangled address and request states, with a routing scheme and an equivalence claim to task superposition, but the whole thing rests on unexamined ideal coherence assumptions.

read the letter

The key takeaway is that this work gives a quantum-native way to address devices in a network by encoding addresses in quantum states paired with request states, which also lets them route using entanglement without classical messages, and they prove this setup is equivalent to running tasks in superposition. What stands out as new is the specific use of address quantum states and request states together, plus the distributed routing protocol that coherently picks routes in a Bell-state network for controlled teleportation. The equivalence to task superposition is framed as a result not in the earlier literature. It does well at removing the classical control overhead and pointing out applications like overlaying different network states. The protocol description is straightforward and builds on standard entanglement ideas. The main soft spot is the reliance on devices being able to reliably prepare, store, and manipulate these states jointly while keeping entanglement and coherence intact across the network. The paper's proof likely assumes ideal conditions here, and without a detailed error analysis or decoherence model in the routing steps, the equivalence holds only under perfect hardware assumptions that current tech doesn't meet. The stress-test concern lands because the abstract doesn't address how errors propagate in the distributed setting. This paper is for quantum information researchers focused on network protocols and architectures. Someone looking for concrete mechanisms to reduce classical traffic in quantum nets would find it useful as a starting point. I would recommend sending it for peer review so the derivations can be checked and the practical limitations clarified.

Referee Report

2 major / 1 minor

Summary. The manuscript proposes a quantum addressing scheme for devices in quantum networks, where each device holds an address quantum state used together with a request quantum state that encodes tasks to be executed. This eliminates classical communication of addresses and operations. The work includes a distributed quantum routing protocol that uses entanglement to coherently select routes in a network of Bell states for controlled teleportation, and concludes with a proof that addressing via quantum states is equivalent to performing tasks in superposition.

Significance. If the equivalence proof is complete and the routing protocol is shown to function without idealization assumptions, the result would enable superposition of network tasks and reduce classical overhead in quantum networks, with potential applications in scalable quantum internet architectures. The entanglement-based coherent routing is a concrete technical contribution if the derivations are fully specified and reproducible.

major comments (2)

[Equivalence proof / conclusion] The equivalence claim (final section) that 'addressing using quantum states is equivalent to performing tasks in superposition' is load-bearing for the paper's main result. The derivation appears to rest on the unexamined assumption that distributed devices can prepare, store, and jointly manipulate entangled address/request states while preserving network-wide coherence during Bell-state routing; without explicit steps showing how this is achieved (e.g., via circuit identities or operator algebra) and without error analysis, the equivalence is conditional rather than unconditional.
[Routing protocol] § on the distributed routing protocol: the description of coherent route selection in the Bell-state network for controlled teleportation lacks the explicit protocol steps, mathematical mapping from address states to route superpositions, or verification that the joint operations commute with the entanglement distribution. This gap prevents verification that the protocol indeed removes all classical communication while maintaining the claimed superposition.

minor comments (1)

[Abstract] Abstract: the sentence 'It turns out that utilizing entanglement...' is informal; replace with a direct statement of the result.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful and constructive review of our manuscript. We address each major comment point by point below, providing clarifications and indicating where revisions will strengthen the presentation.

read point-by-point responses

Referee: [Equivalence proof / conclusion] The equivalence claim (final section) that 'addressing using quantum states is equivalent to performing tasks in superposition' is load-bearing for the paper's main result. The derivation appears to rest on the unexamined assumption that distributed devices can prepare, store, and jointly manipulate entangled address/request states while preserving network-wide coherence during Bell-state routing; without explicit steps showing how this is achieved (e.g., via circuit identities or operator algebra) and without error analysis, the equivalence is conditional rather than unconditional.

Authors: We appreciate the referee highlighting the need for explicitness in the equivalence proof. The final section derives the equivalence by showing that the joint quantum address and request states allow network operations to act as a controlled superposition, with the overall evolution identical to performing the tasks in superposition (via linearity of quantum mechanics). The preparation and joint manipulation are enabled by the entanglement distribution assumed in the network model, and coherence is preserved because the routing acts coherently on the address qubits before any classical readout. We will revise the section to include explicit operator algebra (e.g., showing [U_route, E_entangle] = 0 for the relevant subspaces) and circuit identities demonstrating the mapping. We maintain that the equivalence holds unconditionally under the ideal entanglement assumptions stated in the routing protocol; a full error analysis is outside the scope of this foundational work but could be addressed in follow-up research. revision: partial
Referee: [Routing protocol] § on the distributed routing protocol: the description of coherent route selection in the Bell-state network for controlled teleportation lacks the explicit protocol steps, mathematical mapping from address states to route superpositions, or verification that the joint operations commute with the entanglement distribution. This gap prevents verification that the protocol indeed removes all classical communication while maintaining the claimed superposition.

Authors: We thank the referee for identifying this presentational gap. The protocol encodes the address state |A> to control Bell-pair selection for teleportation, mapping |A> = sum alpha_i |i> to a superposition of routes sum alpha_i |route_i> via controlled-SWAP or controlled-teleportation gates on the address qubits. We will add a detailed step-by-step protocol in the revised manuscript, including the explicit mathematical mapping (address qubits as control registers selecting among pre-shared Bell states) and a commutation proof: the routing unitaries act on disjoint subsystems from the initial entanglement distribution or commute by construction (as they are applied sequentially without intermediate measurements). This ensures the entire process remains fully quantum, eliminating classical address or operation communication while preserving superposition. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained in standard quantum mechanics

full rationale

The paper proposes a quantum addressing scheme using address and request states, presents a distributed routing protocol based on Bell-state entanglement for controlled teleportation, and proves equivalence between quantum-state addressing and superposition tasks. These steps rely on explicit constructions from quantum information primitives (entanglement, teleportation, superposition) without any reduction by construction to fitted parameters, self-definitions, or self-citation chains. The central equivalence claim is derived directly from the protocol definitions rather than presupposing the result. Hardware assumptions about coherence preservation are external requirements, not definitional loops, leaving the mathematical derivation independent and non-circular.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 2 invented entities

The central claim rests on the ability to maintain coherent quantum states and entanglement across devices; no free parameters are introduced, but the scheme postulates address and request states as new operational primitives.

axioms (1)

standard math Standard quantum mechanics, including superposition and entanglement, applies to network-scale devices.
Invoked throughout the description of address states, request states, and the routing protocol.

invented entities (2)

Address quantum state no independent evidence
purpose: Encodes device identity quantum-mechanically to replace classical addressing.
Introduced as the core primitive of the scheme; no independent experimental evidence supplied.
Request quantum state no independent evidence
purpose: Encodes the tasks to be executed together with the address state.
New operational object defined for the protocol; no external verification.

pith-pipeline@v0.9.0 · 5404 in / 1244 out tokens · 58567 ms · 2026-05-10T20:10:20.411874+00:00 · methodology

discussion (0)

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 prove that addressing using quantum states is equivalent to performing tasks in superposition in a quantum network
IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

CNOT between its own address register and the request address register (referred to as selecting a device later). This results in the state ∑ β_i |b_i⟩ |b_i ⊕ a_1⟩

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

22 extracted references · 22 canonical work pages

[1]

Algorithms for quantum computation: discrete logarithms and factoring,

P . Shor, “Algorithms for quantum computation: discrete logarithms and factoring,” in Proceedings 35th Annual Symposium on F oundations of Computer Science , 1994, pp. 124–134

work page 1994
[2]

Quantum internet: From communication to distributed computing!

M. Calefﬁ, A. S. Cacciapuoti, and G. Bianchi, “Quantum internet: From communication to distributed computing!” i n Proceedings of the 5th ACM International Conference on Nano scale Computing and Communication , ser. NANOCOM ’18. New Y ork, NY , USA: ACM, 2018, pp. 3:1–3:4. [Online]. Available: http://doi.acm.org/10.1145/3233188.3233224

work page doi:10.1145/3233188.3233224 2018
[3]

Quantum Internet: Networking Chal lenges in Distributed Quantum Computing,

A. S. Cacciapuoti, M. Calefﬁ, F. Tafuri, F. Saverio Catal iotti, S. Gher- ardini, and G. Bianchi, “Quantum Internet: Networking Chal lenges in Distributed Quantum Computing,” ArXiv e-prints, p. arXiv:1810.08421, Oct. 2018

work page arXiv 2018
[4]

Shor and John Preskill , Date-Added =

P . W. Shor and J. Preskill, “Simple Proof of Security of the BB84 Quantum Key Distribution Protocol,” Phys. Rev. Lett., vol. 85, pp. 441–444, Jul 2000. [Online]. Available: http://link.aps.org/doi/10.1103/PhysRevLett.85.441

work page doi:10.1103/physrevlett.85.441 2000
[5]

The quantum internet,

H. J. Kimble, “The quantum internet,” Nature, vol. 453, no. 7198, pp. 1023–1030, Jun 2008. [Online]. Available: http://dx.doi.org/10.1038/nature07127

work page doi:10.1038/nature07127 2008
[6]

Modular architectures for quantum networks,

A. Pirker, J. Walln¨ ofer, and W. D¨ ur, “Modular architectures for quantum networks,” New J. Phys. , vol. 20, no. 5, p. 053054, 2018. [Online]. Available: http://stacks.iop.org/1367-2630/20/i=5/a=053054

work page 2018
[7]

V an Meter, Quantum Error Correction-Based Repeaters

R. V an Meter, Quantum Error Correction-Based Repeaters . John Wiley & Sons, Ltd, 2014, pp. 219–236. [Online]. Available: http://dx.doi.org/10.1002/9781118648919.ch11

work page doi:10.1002/9781118648919.ch11 2014
[8]

Recursive quantu m repeater networks,

R. V an Meter, J. Touch, and C. Horsman, “Recursive quantu m repeater networks,” NII Journal , no. 8, pp. 65–79, 3 2011. [Online]. Available: doi:10.2201/NiiPi.2011.8.8

work page doi:10.2201/niipi.2011.8.8 2011
[9]

Genuine quant um networks with superposed tasks and addressing,

J. Miguel-Ramiro, A. Pirker, and W. D¨ ur, “Genuine quant um networks with superposed tasks and addressing,” npj Quantum Information, vol. 7, no. 1, p. 135, Sep 2021. [Online]. Available: https://doi.org/10.1038/s41534-021-00472-5

work page doi:10.1038/s41534-021-00472-5 2021
[10]

Prior entanglement between senders enabl es perfect quantum network coding with modiﬁcation,

M. Hayashi, “Prior entanglement between senders enabl es perfect quantum network coding with modiﬁcation,” Phys. Rev. A , vol. 76, p. 040301, Oct 2007. [Online]. Available: https://link.aps.org/doi/10.1103/PhysRevA.76.040301

work page doi:10.1103/physreva.76.040301 2007
[11]

Designing quantum repeater ne tworks,

R. V . Meter and J. Touch, “Designing quantum repeater ne tworks,” IEEE Communications Magazine, vol. 51, no. 8, pp. 64–71, August 2013

work page 2013
[12]

A quantum network stack and proto cols for reliable entanglement-based networks,

A. Pirker and W. D¨ ur, “A quantum network stack and proto cols for reliable entanglement-based networks,” New Journal of Physics , vol. 21, no. 3, p. 033003, mar 2019. [Online]. Available: https://dx.doi.org/10.1088/1367-2630/ab05f7

work page doi:10.1088/1367-2630/ab05f7 2019
[13]

A link layer p rotocol for quantum networks,

A. Dahlberg, M. Skrzypczyk, T. Coopmans, L. Wubben, F. Rozpundeﬁneddek, M. Pompili, A. Stolk, P . Pawełczak, R. K negjens, J. de Oliveira Filho, R. Hanson, and S. Wehner, “A link layer p rotocol for quantum networks,” in Proceedings of the ACM Special Interest Group on Data Communication , ser. SIGCOMM ’19. New Y ork, NY , USA: Association for Computing M...

work page doi:10.1145/3341302 2019
[14]

Towards large-scale quant um networks,

W. Kozlowski and S. Wehner, “Towards large-scale quant um networks,” in Proceedings of the Sixth Annual ACM International Conferen ce on Nanoscale Computing and Communication , ser. NANOCOM ’19. New Y ork, NY , USA: Association for Computing Machinery, 201 9. [Online]. Available: https://doi.org/10.1145/3345312. 3345497

work page doi:10.1145/3345312
[15]

Designing a q uantum network protocol,

W. Kozlowski, A. Dahlberg, and S. Wehner, “Designing a q uantum network protocol,” in Proceedings of the 16th International Conference on Emerging Networking EXperiments and Technologies , ser. CoNEXT ’20. New Y ork, NY , USA: Association for Computing Machinery , 2020, p. 1–16. [Online]. Available: https://doi.org/10.1145/3 386367.3431293

work page doi:10.1145/3 2020
[16]

Quantum internet protocol stack: A comprehensive survey,

J. Illiano, M. Calefﬁ, A. Manzalini, and A. S. Cacciapuo ti, “Quantum internet protocol stack: A comprehensive survey, ” Computer Networks , vol. 213, p. 109092, 2022. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S1389128622002250

work page 2022
[17]

Quantum internet addressing,

A. S. Cacciapuoti, J. Illiano, M. Viscardi, and M. Calef ﬁ, “Quantum internet addressing,” 2023

work page 2023
[18]

Design and implementation of the illinois express quantum metropo litan area network,

J. Chung, E. M. Eastman, G. S. Kanter, K. Kapoor, N. Lauk, C. H. Pe˜ na, R. K. Plunkett, N. Sinclair, J. M. Thomas, R. V alivart hi, S. Xie, R. Kettimuthu, P . Kumar, P . Spentzouris, and M. Spiropulu, “ Design and implementation of the illinois express quantum metropo litan area network,” IEEE Transactions on Quantum Engineering , vol. 3, pp. 1–20, 2022

work page 2022
[19]

A resource-centric, task-based approach to quantum network control,

A. Pirker, B. Munoz, and W. D¨ ur, “A resource-centric, t ask-based approach to quantum network control,” 2025. [Online]. Avai lable: https://arxiv.org/abs/2507.12030

work page arXiv 2025
[20]

The quant-net testbed developme nt and pre- liminary results,

D. Schon, P . Umesh, Y .-W. Cheah, S.-Y . Y u, E. Kissel, R. V alivarthi, E. Saglamyurek, L. Ramakrishnan, W. Wu, A. Sipahigil, M. Spi ropulu, H. H¨ affner, and I. Monga, “The quant-net testbed developme nt and pre- liminary results,” in 2024 IEEE International Conference on Quantum Computing and Engineering (QCE) , vol. 01, 2024, pp. 1799–1808

work page 2024
[21]

Quantum internet arch itecture: unlocking quantum-native routing via quantum addressing,

M. Calefﬁ and A. S. Cacciapuoti, “Quantum internet arch itecture: unlocking quantum-native routing via quantum addressing, ” 2025. [Online]. Available: https://arxiv.org/abs/2507.19655

work page arXiv 2025
[22]

A quantu m inter- net architecture,

R. V an Meter, R. Satoh, N. Benchasattabuse, K. Teramoto , T. Matsuo, M. Hajduˇ sek, T. Satoh, S. Nagayama, and S. Suzuki, “A quantu m inter- net architecture,” in 2022 IEEE International Conference on Quantum Computing and Engineering (QCE) , 2022, pp. 341–352

work page 2022