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Twin-Field Quantum Network Coding for Multi-Party Key Distribution Cover

Twin-Field Quantum Network Coding for Multi-Party Key Distribution

By: Yuchen Liu,  Tao Shang and  Keyu Xiong  
Open Access
|Dec 2025

Figures & Tables

Figure 1.

The basic structure of TF-QKD.
The basic structure of TF-QKD.

Figure 2.

Butterfly network model for twin-field transmission.
Butterfly network model for twin-field transmission.

Figure 3.

Quantum operations at each node in the butterfly network.
Quantum operations at each node in the butterfly network.

Figure 4.

Classical transmission after the coherent measurements.
Classical transmission after the coherent measurements.

Figure 5.

Comparison of point-to-point key rates.
Comparison of point-to-point key rates.

Figure 6.

Comparison of multi-party key rates.
Comparison of multi-party key rates.

Comparison with other QNC schemes_

QNC schemeQuantum resourcesPossibility to be used in QKDRelationship between key rate and transmittance
XQQ [2]Non-orthogonal quantum statesNo-
QNC based on PE scheme [3,6,12]Pre-shared entanglementsPossibleRη
QNC with repeaters [11]Quantum repeatersPossibleRη1/n
QNC based on MBQC [5,9]Cluster statesNo-
Our schemeWeak coherent statesYesRη1/2

Comparison of channel usage between TF-QNC and TF-QKD_

SchemeNon-bottleneck channelsBottleneck channelAverage total times
Point-to-Point TF-QKD2 channels × 226n1
Point-to-Point TF-QNC12 channels × 2152n15\sqrt 2 {n_1}
Multi-Party TF-QKD24 channels × 6428n2
Multi-Party TF-QNC4 channels × 219γn2

Comparison of quantum states usage between TF-QNC and TF-QKD_

SchemeQuantum states in one executionAverage total number
Point-to-Point TF-QKD2 nodes × 12n1
Point-to-Point TF-QNC2 nodes × 122n12\sqrt 2 {n_1}
Multi-Party TF-QKD4 nodes ×312n2
Multi-Party TF-QNC4 nodes × 14γn2
DOI: https://doi.org/10.2478/qic-2025-0027 | Journal eISSN: 3106-0544 | Journal ISSN: 1533-7146
Language: English
Page range: 488 - 508
Submitted on: Jul 4, 2025
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Accepted on: Sep 29, 2025
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Published on: Dec 31, 2025
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year

© 2025 Yuchen Liu, Tao Shang, Keyu Xiong, published by Cerebration Science Publishing Co., Limited
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.