Advancing Quantum Cryptography: A Deep Dive into the Security of Three-Level Unitary Operations in Quantum Secret Sharing


Quantum Secret Sharing (QSS) is a concept in the field of quantum cryptography, which is a branch of cryptography that uses the principles of quantum mechanics to secure information. The idea of secret sharing, in general, involves dividing a secret into parts and distributing these parts to multiple participants. None of the participants can know the whole secret by themselves, but they can collectively reconstruct it. QSS utilizes entangled quantum states. These are special states in which the properties of one quantum particle are directly related to the properties of another, no matter how far apart they are. This is known as quantum entanglement. The secret (such as a cryptographic key) is encoded into a quantum state. This state is then divided into parts (sub-states), which are distributed to the participants. One of the main advantages of QSS is its inherent security. The laws of quantum mechanics state that measuring a quantum state inevitably alters it. Thus, any eavesdropping attempt on the quantum states being shared will be detectable. When the participants want to reconstruct the secret, they bring their parts of the quantum state together. By performing specific quantum operations and measurements, they can retrieve the original secret.

Indeed, QSS protocols serve as the backbone for secure quantum communication. Traditional binary quantum systems (qubits) have long dominated this space, but the introduction of qutrits – three-level quantum systems – offers a new dimension of complexity and security. The researchers’ decision to explore QSS protocols based on qutrits stems from the promise of enhanced security features that these higher-dimensional systems can potentially offer. In a new study published in the Frontiers in Physics led by Associate Professor Juan Xu, Xi Li, Yunguang Han, Yuqian Zhou, Zhihao Liu, Zhengye Zhang and Yinxiu Song from the Nanjing University of Aeronautics and Astronautics, the researchers conducted a comprehensive study on the security of three-level unitary operations in quantum secret sharing (QSS) protocols based on qutrits, focusing on their resistance to Bell-state attacks.

The team examined a three-level quantum system, known as a qutrit. They explored the Z-basis and X-basis of such a system and defined three-level Bell states. These states form a complete orthogonal basis in a three-level system, vital for analyzing the security of QSS protocols based on qutrits. They outlined a general QSS protocol that involves preparing, transforming, and measuring qutrits. The protocol included steps where multiple parties (Bobs) perform local unitary operations on the qutrits based on certain values. The authors presented a detailed schematic of a Bell-state attack. This attack is a significant threat model where a dishonest participant (Bob) attempts to gain unauthorized access to the shared secret. The researchers described how such an attack is executed and its potential effects on the security of the QSS protocol. They also analyzed the security of one-step and two-step three-level unitary operations. This involved calculating the minimum failure probability of a Bell-state attack, which serves as a quantitative measure of security. Various unitary operations were examined to determine how they influence the protocol’s security against such attacks.

The authors found that the security of the QSS protocol varies based on the choice of unitary operations. They identified specific sets of unitary operations that offer different levels of security, quantified by the minimum failure probability. For security of Two-Step Three-Level Unitary Operations, in such scenario, they observed that the combination of unitary operations impacts the security. The researchers divided the combinations into categories and calculated the minimum failure probability for each, leading to insights into how different combinations affect security. The paper provided a comparative analysis of the security afforded by different sets of unitary operations. This analysis offers guidance for selecting the most secure combinations in practical QSS implementations based on qutrits. The findings have significant implications for the design and implementation of secure quantum cryptographic protocols, especially in scenarios that use high-dimensional states like qutrits.

The new study marks a significant stride in quantum cryptography. The findings provide a deeper understanding of the security dynamics in high-level quantum cryptographic schemes. The study’s rigorous quantitative approach offers a solid foundation for designing more secure quantum secret sharing protocols, enhancing the overall robustness of quantum communication networks. This work not only contributes to the theoretical advancement in quantum cryptography but also paves the way for practical implementations, ensuring robust, secure quantum communication in the future.

In conclusion, the study by Associate Professor Juan Xu and colleagues represents a crucial step in the evolution of quantum cryptography, offering valuable insights into the security mechanisms of three-level unitary operations in quantum secret sharing. Its methodological rigor and comprehensive analysis underscore the potential of advanced quantum cryptographic protocols in safeguarding information in an increasingly digital world.

Advancing Quantum Cryptography: A Deep Dive into the Security of Three-Level Unitary Operations in Quantum Secret Sharing – Advances in Engineering

About the author

Juan Xu is an Associate Professor with the College of Computer Science and Technology, Nanjing University of Aeronautics and Astronautics, Nanjing, China. She received her Ph.D. in computer software and theory from Southeast University, Nanjing, China, in 2012, under the supervision of Professor Hanwu Chen. And since then, she has served as a teacher in Nanjing University of Aeronautics and Astronautics. From August 2017 to August 2018, Juan was a Visiting Scholar of the Institute for Quantum Computing at University of Waterloo, ON, Canada (the collaborative professor was Michele Mosca, and he gave the helpful feedback for the above work). Her research interests include quantum cryptography, quantum computing, classical and quantum artificial intelligence, etc.


Xu J, Li X, Han Y, Zhou Y, Liu Z, Zhang Z and Song Y (2023), Quantitative security analysis of three-level unitary operations in quantum secret sharing without entanglement. Front. Phys. 11:1213153. doi: 10.3389/fphy.2023.1213153.

Go to Front. Phys.

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