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Quantum Information Processing

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

Sachi Gupta, Aman Sinha, Sumit Kumar Pandey

Published Feb 9, 2024• 9 citations
Publisher
DOI
10.1007/s11128-024-04265-5

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Quantum secret sharing(QSS) is a procedure of sharing classical information or quantum information by using quantum states. This paper presents how to use a [2 k − 1, 1, k ] quantum error-correcting code (QECC) to implement a quantum ( k , 2 k − 1) threshold scheme. It also takes advantage of classical enhancement of the [2 k − 1, 1, k ] QECC to establish a QSS scheme which can share classical information and quantum information simultaneously. Because information is encoded into QECC, these schemes can prevent intercept-resend attacks and be implemented on some noisy channels.
Abstract Quantum secret sharing has wide application prospects in quantum communication, quantum network and other fields. It can provide a secure and reliable information sharing method for multi-party communication. In this paper, we mainly study the connection mechanism between the quantum secret-sharing scheme and quantum error-correcting codes. Firstly, we give the necessary and sufficient conditions for the existence of quantum error-correcting codes based on group algebra theory. Secondly, we give the corresponding quantum secret sharing scheme model with local quantum operation and classical communication capability can be constructed by any given quantum error-correcting codes. The advantage of this model is that the corresponding quantum secret-sharing scheme can be found for any quantum error-correcting code.