基于矩阵乘积压缩态的动态可扩展秘密共享方案

Dynamic and scalable secret sharing schemes based on matrix product compressed states

目前,基于纠缠态的量子秘密共享(quantum secret sharing,QSS)方案未充分利用纠缠态的概率振幅潜力.然而,纠缠态的概率振幅是量子信息学的一个关键特性,在量子计算和量子通信等领域有着广泛的应用潜力.值得注意的是,纠缠态可以通过矩阵乘积态(matrix product state,MPS)有效表达.利用MPS对纠缠态进行表征,能够准确地揭示与概率振幅相关的纠缠特性.本研究证明利用MPS表征纠缠态,可以将一个W态压缩为一个单光子和一个矩阵,展示一种新的技术路径.此外,本研究还提出MPS与秘密共享方案之间的创新互操作性,即通过压缩允许量子份额与共享的量子态之间形成非一对一的映射关系.这种方法可能提供一种更高效的方式来实现量子信息的编码和传输,对于量子秘密共享尤为重要.同时,我们提出的QSS方案具有动态特性,能够根据需要轻松地添加或移除参与者,以更好地适应参与者需求的变化,并在实际应用场景中展现出更高的实用性和适应性.本文的方案能够在保持高效纠缠利用的同时,满足系统的多元需求,包括但不限于通信安全性、数据传输率和系统的可扩展性.

Currently,quantum secret sharing(QSS)schemes based on entangled states have not yet fully utilized the potential of the probability amplitude of entangled states.However,the probability amplitude is a key characteristic of quantum information science and possesses significant application prospects in the fields of quantum computing and quantum communication.It is worth noting that entangled states can be effectively represented by matrix product states(MPSs).The representation of entangled states using MPS can precisely reveal the entanglement characteristics closely related to the probability amplitude.This study first focuses on the representation of the W state by using MPS,an approach that allows us to determine the key conditions for W state to achieve quantum advantage in QSS.Subsequently,this research demonstrates that by representing entangled states with MPS,a W state can be compressed into a single photon state and a simplified matrix form,presenting an innovative technical path.Moreover,one of the most attractive features of our proposed QSS scheme is its ability to compress multiple different quantum states(represented by photons)into a unified state represented by a single photon.This characteristic endows our scheme with scalability and flexibility,meaning that the group of participants can be easily expanded or reduced according to their specific needs.The addition of new participants is managed by Alice,who is responsible for the distribution of quantum state shares.On the other hand,when a participant leaves the group,their old quantum state share can be simply ignored in the process of recovering the secret's quantum state,thereby simplifying the management process.Through this strategy,we can not only make effective use of entangled resources but also meet the various requirements of the system,including but not limited to communication security,data transfer rates,and system scalability.This research provides new perspectives and possibilities for the field of quantum information science and may have a significant influence on the development of the field.