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EPJ Quantum Technology

Quantum network coding against pollution attacks based on quantum state sharing

Zhenzhen Li, Ming-Kui Liu, Bo Gao, Zi-Chen Li

Published Jul 9, 2026• 0 citations

Abstract

Abstract Quantum network coding (QNC) can encode and decode quantum information, thereby improving the communication efficiency. However, it is vulnerable to pollution attacks, which will lead to invalid transmission throughout the quantum network. Inspired by the idea of quantum state sharing (QSTS), we introduce QSTS into QNC for the first time to address security issues such as pollution attacks. Subsequently, a novel QNC scheme against pollution attacks based on QSTS is proposed in the paper. In the scheme, the first intermediate node encodes quantum states and performs the first round of sharing. Meanwhile, it conducts an XOR operation on the classical information. The second intermediate node encodes quantum states and performs the second round of sharing. Meanwhile, it duplicates the classical information. Different from the first one, it needs to distribute the quantum state to two receivers by means of quantum teleportation, measurement by using the designed basis, and unitary operations. Finally, the receiver performs the third round of sharing on the quantum state, then verifies the existence of pollution attacks by comparing the quantum information with the classical information. Through performance analysis, the proposed scheme can realize that receivers can receive the quantum state from senders with the fidelity of 1 and the success probability of 1 simultaneously. In addition, we also apply the scheme to the extended butterfly network, which demonstrates superior extensibility and practicability.

DOI: 10.1140/epjqt/s40507-026-00539-2

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Quantum network coding is vulnerable to pollution attacks, especially when using classical channel as auxiliary resource. On this basis, this letter proposes a secure quantum network coding scheme against pollution attacks. The scheme uses quantum homomorphic signature for the efficient authentication of different data sources so as to detect pollution attacks in the butterfly network. Furthermore, with the help of trusted intermediate nodes, it can locate a corrupt data source. Analysis results show that the proposed quantum network coding scheme can defend against pollution attacks with high fidelity, fewer resource consumption, and lower rate region.

In order to improve the security and transmission efficiency of quantum network coding (QNC), we propose a new QNC scheme based on butterfly network. The scheme uses two groups of GHZ states to distribute quantum entangled states through intermediate nodes, so as to establish the connection between multiple nodes and achieve safe and reliable quantum traffic. This paper can not only improve the security of QNC, but also reduce the transmission of particles and improve the anti-interference ability of information. Compared with the traditional network coding method based on a priori entanglement, our scheme is a better attempt.

Abstract Quantum network coding (QNC) aims at alleviating quantum communication congestion in quantum networks. Although several QNC protocols have been presented, they cannot meet the practical requirements that part of source nodes intend to transmit their quantum states with same or different qubit numbers via the bottleneck network simultaneously. Here, the study presents a flexible QNC protocol by using quantum multiplexing. First, the entangled pairs are generated between adjacent nodes in a heralded way by using quantum multiplexing. Then the quantum memories of the source nodes and the ones of the corresponding target nodes are entangled when the intermediate nodes execute multiple rounds of entanglement swapping operations on their quantum memories. Finally, the quantum states are transmitted from the source nodes to their corresponding target nodes by means of quantum teleportation. Compared with the existing protocols, the protocol allows an arbitrary part of the source nodes to transmit their quantum states with same or different qubit numbers via the bottleneck network simultaneously, thereby exhibiting its flexibility.

Classical network coding uses encoding of information over networks to achieve secure and high throughput communication with low latency. Its quantum analog, namely Quantum Network Coding (QNC) is a promising protocol to achieve quantum communication over quantum networks. In this paper, we propose a method for establishing QNC in Measurement-Based Quantum Computing (MBQC), which is a universal quantum computational model. We demonstrate that the problem of multiple unicast or multiple multicast of distinct computational basis states over a quantum network can be solved by simulating existing classical networks, with the CNOT implementation in MBQC as a basis for transmitting and encoding of states. We also show how it can be further extended to simultaneously distribute the Bell pairs and Greenberger–Horne–Zeilinger (GHZ) states required for quantum communication between distant transmitter and corresponding receiver nodes of a network.

the purpose of this paper is to promote a butterfly quantum network coding scheme for remote state preparation of multi-qudit states. Firstly, we perform channel preparation and amplitude modulation; secondly, each sender simultaneously performs projection measurement; thirdly, both senders send measurement results as precoding information and auxiliary information to the intermediate node and the neighboring receivers respectively; fourthly, the first intermediate node performs encoding operation and sends the encoded information to both receivers via next intermediate node. Finally, by decoding the coded information with auxiliary information, two receivers perform corresponding unitary operations to recover the target multi-qudit quantum states. Compared with other schemes, our scheme can enhance the throughput and transmission efficiency of communication network for remote state preparation of multi-qudit states.

Quantum network coding is expected to enable multiple quantum data packets to be fused before the transmission via the bottleneck channel in order to improve the transmission efficiency and the total throughput of quantum networks. Although several quantum network coding schemes have been constructed, they are unable to meet the practical application requirements due to the fact that they lack a complete security solution. To tackle this issue, a practical secure quantum network coding scheme is constructed. Compared with existing methods, the proposed quantum network coding scheme is more practical and most importantly it can provide complete security against both information leakage and pollution attacks, which greatly contributes to global quantum communication networks.