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Quantum secret sharing (QSS), as a quantum extension of classical secret sharing, uses the basic principles of quantum mechanics to share information safely among multiple parties, providing a new paradigm for information security. As a key foundation for secure multiparty quantum communication and distributed quantum computing, QSS has attracted considerable attention since its emergence. Currently, research in this field includes both classical and quantum scenarios, and continuous progress has been made in both theoretical and experimental aspects. This paper first reviews the current development of QSS for classical information. In this regard, significant and parallel progress has been made in both discrete-variable QSS and continuous-variable QSS. The QSS protocols for sharing classical information, from entangled states to single photons and then to coherent light, have been continuously optimized to better utilize available resources and achieve more efficient implementation under current technological conditions. Meanwhile, round-robin, measurement-device-independent, and other protocols have been steadily improving the security of QSS. Next, one will focus on QSS scheme for quantum secrets, which begins with the symmetry of access structures and introduces basic (k, n) threshold protocols, dynamic schemes that support adaptive agent groups, and symmetric quantum information splitting through entanglement. It further introduces hierarchical quantum secret sharing schemes for asymmetric splitting of quantum information. Considering practical laboratory conditions of quantum states as resources, an overall discussion is conducted on quantum secret sharing with graph states. Afterwards, the design of a continuous-variable scheme for quantum secret sharing is outlined, and entanglement state sharing and quantum teleportation between multiple senders and receivers are introduced. Finally, this review discusses and outlines the future development directions of QSS, thereby inspiring readers to further study and explore the relevant subjects.
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Keywords:
- quantum secret sharing /
- quantum communication /
- quantum entanglement /
- multiparty quantum protocols
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Alice $ |+x\rangle $ $ |-x\rangle $ $ |+y\rangle $ $ |-y\rangle $ Bob $ |+x\rangle $ $ |+x\rangle $ $ |-x\rangle $ $ |-y\rangle $ $ |+y\rangle $ $ |-x\rangle $ $ |-x\rangle $ $ |+x\rangle $ $ |+y\rangle $ $ |-y\rangle $ $ |+y\rangle $ $ |-y\rangle $ $ |+y\rangle $ $ |-x\rangle $ $ |+x\rangle $ $ |-y\rangle $ $ |+y\rangle $ $ |-y\rangle $ $ |+x\rangle $ $ |-x\rangle $ 
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QSS方案 特点 使用纠缠态的QSS 由于纠缠特性, 即使光源部分被攻击者控制, 只要测量端能够被完美表征并进行测量错误率即可获得安全的秘密共享. 但目前实验上高效制备纠缠态仍具有较大困难 使用单光子的QSS 相比于纠缠态, 单光子更容易制备和分发, 更具实验性和扩展性. 但仍与目前的通信光纤有适配性差异且容易受到特洛伊木马的攻击 使用相干光的QSS 实验实现简单, 与标准光纤适配更容易实现远距离传输, 具有高稳定性和易操作性. 但相干光存在多光子成分, 无法抵御光子数分裂攻击 离散变量的QSS 利用光子偏振态$ |H\rangle $和$ |V\rangle $或轨道角动量来编码密钥比特, 系统对损耗不敏感、测量和判别精度高. 但信道容量低、单光子制备困难 连续变量的QSS 利用光场的正交分量$ \hat{x} $和$ \hat{p} $来编码密钥比特, 相比于离散变量可以确定性实现. 但大多数方案要求独立激光源及激光源之间的信号同步, 并且易受到本振攻击 环回QSS 不用监测信号扰动, 密钥率能打破Pirandola-Laurenza-Ottaviani-Banchi界限. 但需要使用可变延迟马赫-曾德尔干涉仪限制了其实际应用 测量设备无关的QSS 能够消除测量端设备不完美带来的攻击风险, 有效增强系统的安全性. 但大多数协议传输效率仍然会随着用户数量的增加呈指数级下降 设备无关的QSS 能够消除所有实际不完美设备的安全漏洞. 但目前协议的性能仍然较低, 尚未有效实现
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