On the equivalence between sharing quantum and classical secrets, and error correction

Abstract

We present a general scheme for sharing quantum secrets, and an extension to sharing classical secrets, which contain all known quantum secret sharing schemes. In this framework we show the equivalence of existence of both schemes, that is, the existence of a scheme sharing a quantum secret implies the extended classical secret sharing scheme works, and vice versa. As a consequence of this we find new schemes sharing classical secrets for arbitrary access structures. We then clarify the relationship to quantum error correction and observe several restrictions thereby imposed, which for example indicates that for pure state threshold schemes the share size $q$ must scale with the number of players $n$ as $q\ge \sqrt{n}$. These results also provide a new way of searching for quantum error correcting codes.

7 pages, 2 figures, updated to journal version (improved discussions, and general proof of security for the RCQ protocol)

References in corpus (6)

• Quantum secret sharing with qudit graph states
• Uncertainty, Monogamy, and Locking of Quantum Correlations
• Non-Threshold Quantum Secret Sharing Schemes in the Graph State Formalism
• Reducing the quantum communication cost of quantum secret sharing
• Generalized Semi-Quantum Secret Sharing Schemes
• Information Flow in Secret Sharing Protocols

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• Subtraction better than addition: Entanglement in multimode squeezed vacuum post-interface with photons
• Unitary Reconstruction of Secret for Stabilizer Based Quantum Secret Sharing
• Verification of graph states in an untrusted network
• Constructive Interference Between Disordered Couplings Enhances Multiparty Entanglement in Quantum Heisenberg Spin Glass Models
• Unified Approach to Secret Sharing and Symmetric Private Information Retrieval with Colluding Servers in Quantum Systems
• Random coding for sharing bosonic quantum secrets
• Certifying dimension of quantum systems by sequential projective measurements
• Classical Access Structures of Ramp Secret Sharing Based on Quantum Stabilizer Codes
• Coding Theoretic Construction of Quantum Ramp Secret Sharing
• Quantum Stabilizer Codes Can Realize Access Structures Impossible by Classical Secret Sharing
• Quantum secret sharing and Mermin operator
• Message Randomization and Strong Security in Quantum Stabilizer-Based Secret Sharing for Classical Secrets
• Exploring Quantum Supremacy in Access Structures of Secret Sharing by Coding Theory
• Measurement-free reconstruction circuit of quantum secrets in quantum secret sharing
• Sharing classical secrets with continuous-variable entanglement: Composable security and network coding advantage
• Access structure in graphs in high dimension and application to secret sharing
• Geometric Graph-Theoretic Aspects of Quantum Stabilizer Codes