Currently, Quantum Secret Sharing (QSS) schemes based on entangled states have not yet fully harnessed the potential of the probability amplitude of entangled states. However, the probability amplitude is a key characteristic of quantum information science and holds 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 (MPS). 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 using Matrix Product States (MPS), an approach that allows us to determine the key conditions for W state to achieve quantum advantage in Quantum Secret Sharing (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 efficiently utilize entanglement resources but also meet the diverse needs 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 impact on promoting the development of the field.