A resilient m-qubit quantum secret sharing scheme using quantum error correction code

Proposed by Hillery et al., Quantum Secret Sharing (QSS) is a technique used to break a quantum secret into multiple pieces (called Shares), such that any proper subset of the pieces does not reveal any information about the original secret. The secret can be reconstructed only when all of the pieces are combined together. However, most of the QSS protocols assume that the shares are untampered, hence fail to regenerate the original secret if some of the shares are damaged due to several reasons like cheating participants, eavesdropping, etc. In order to tackle this practical challenge, Resilient Quantum Secret Sharing (RQSS) protocols are required. In this paper, we propose an RQSS protocol that uses Quantum Error Correcting Codes (QECC) for share generation and secret reconstruction. Our protocol generates n shares of a m-qubit quantum secret, owned by the dealer, and distributes it among n participants; moreover, it can regenerate the original secret even if \(k < n\) $k<n$ shares are damaged. To the best of our knowledge, no such generalized protocol exists in the available literature.