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Verifiable quantum secret sharing scheme based on orthogonal product states |
| Chen-Ming Bai(白晨明)†, Lu Liu(刘璐), and Sujuan Zhang(张素娟) |
| Department of Mathematics and Physics, Shijiazhuang Tiedao University, Shijiazhuang 050043, China |
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Abstract In the domain of quantum cryptography, the implementation of quantum secret sharing stands as a pivotal element. In this paper, we propose a novel verifiable quantum secret sharing protocol using the $d$-dimensional product state and Lagrange interpolation techniques. This protocol is initiated by the dealer Alice, who initially prepares a quantum product state, selected from a predefined set of orthogonal product states within the $\mathbb{C}^d \otimes \mathbb{C}^d$ framework. Subsequently, the participants execute unitary operations on this product state to recover the underlying secret. Furthermore, we subject the protocol to a rigorous security analysis, considering both eavesdropping attacks and potential dishonesty from the participants. Finally, we conduct a comparative analysis of our protocol against existing schemes. Our scheme exhibits economies of scale by exclusively employing quantum product states, thereby realizing significant cost-efficiency advantages. In terms of access structure, we adopt a $(t,n)$-threshold architecture, a strategic choice that augments the protocol's practicality and suitability for diverse applications. Furthermore, our protocol includes a rigorous integrity verification mechanism to ensure the honesty and reliability of the participants throughout the execution of the protocol.
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Received: 21 December 2023
Revised: 04 March 2024
Accepted manuscript online: 15 March 2024
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PACS:
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03.67.-a
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(Quantum information)
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03.65.Ud
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(Entanglement and quantum nonlocality)
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| Fund: This work was supported by the National Natural Science Foundation of China (Grant No. 12301590) and the Natural Science Foundation of Hebei Province (Grant No. A2022210002). |
Corresponding Authors:
Chen-Ming Bai
E-mail: baichm@stdu.edu.cn
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Cite this article:
Chen-Ming Bai(白晨明), Lu Liu(刘璐), and Sujuan Zhang(张素娟) Verifiable quantum secret sharing scheme based on orthogonal product states 2024 Chin. Phys. B 33 070302
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