Generalized Semi-Quantum Secret Sharing Schemes

Abstract

We investigate quantum secret sharing schemes constructed from $[[n,k,\delta ]{]}_D$ non-binary stabilizer quantum error correcting codes with carrier qudits of prime dimension $D$. We provide a systematic way of determining the access structure, which completely determines the forbidden and intermediate structures. We then show that the information available to the intermediate structure can be fully described and quantified by what we call the *information group*, a subgroup of the Pauli group of $k$ qudits, and employ this group structure to construct a method for hiding the information from the intermediate structure via twirling of the information group and sharing of classical bits between the dealer and the players. Our scheme allows the transformation of a ramp (intermediate) quantum secret sharing scheme into a semi-quantum perfect secret sharing scheme with the same access structure as the ramp one but without any intermediate subsets, and is optimal in the amount of classical bits the dealer has to distribute.

Replaced by published version, typos corrected

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Cited by in corpus (11)

• Absolutely Maximally Entangled States: Existence and Applications
• On the equivalence between sharing quantum and classical secrets, and error correction
• Verifiable Hybrid Secret Sharing With Few Qubits
• Accessing quantum secrets via local operations and classical communication
• A Generalized Information Theoretical Model for Quantum Secret Sharing
• Classical Access Structures of Ramp Secret Sharing Based on Quantum Stabilizer Codes
• Secure and authenticated quantum secret sharing
• Message Randomization and Strong Security in Quantum Stabilizer-Based Secret Sharing for Classical Secrets
• Deterministic Twirling with Low Resources
• Access structure in graphs in high dimension and application to secret sharing
• Quantum Access Structure and Secret Sharing