Non-Threshold Quantum Secret Sharing Schemes in the Graph State Formalism

Abstract

In a recent work, Markham and Sanders have proposed a framework to study quantum secret sharing (QSS) schemes using graph states. This framework unified three classes of QSS protocols, namely, sharing classical secrets over private and public channels, and sharing quantum secrets. However, most work on secret sharing based on graph states focused on threshold schemes. In this paper, we focus on general access structures. We show how to realize a large class of arbitrary access structures using the graph state formalism. We show an equivalence between $[[n,1]]$ binary quantum codes and graph state secret sharing schemes sharing one bit. We also establish a similar (but restricted) equivalence between a class of $[[n,1]]$ Calderbank-Shor-Steane (CSS) codes and graph state QSS schemes sharing one qubit. With these results we are able to construct a large class of quantum secret sharing schemes with arbitrary access structures.

LaTeX, 6 pages

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• Implementation of quantum secret sharing and quantum binary voting protocol in the IBM quantum computer
• Device Independent Quantum Secret Sharing in Arbitrary Even Dimension
• Unitary Reconstruction of Secret for Stabilizer Based Quantum Secret Sharing
• On Weak Odd Domination and Graph-based Quantum Secret Sharing
• Unified Approach to Secret Sharing and Symmetric Private Information Retrieval with Colluding Servers in Quantum Systems
• Classical Access Structures of Ramp Secret Sharing Based on Quantum Stabilizer Codes
• Coding Theoretic Construction of Quantum Ramp Secret Sharing
• Advance sharing of quantum shares for classical secrets
• Message Randomization and Strong Security in Quantum Stabilizer-Based Secret Sharing for Classical Secrets
• Measurement-free reconstruction circuit of quantum secrets in quantum secret sharing
• $(t,n)$ Threshold $d$-level quantum secret sharing based on quantum Fourier transformation