Information Flow in Secret Sharing Protocols

Abstract

The entangled graph states have emerged as an elegant and powerful quantum resource, indeed almost all multiparty protocols can be written in terms of graph states including measurement based quantum computation (MBQC), error correction and secret sharing amongst others. In addition they are at the forefront in terms of implementations. As such they represent an excellent opportunity to move towards integrated protocols involving many of these elements. In this paper we look at expressing and extending graph state secret sharing and MBQC in a common framework and graphical language related to flow. We do so with two main contributions. First we express in entirely graphical terms which set of players can access which information in graph state secret sharing protocols. These succinct graphical descriptions of access allow us to take known results from graph theory to make statements on the generalisation of the previous schemes to present new secret sharing protocols. Second, we give a set of necessary conditions as to when a graph with flow, i.e. capable of performing a class of unitary operations, can be extended to include vertices which can be ignored, pointless measurements, and hence considered as unauthorised players in terms of secret sharing, or error qubits in terms of fault tolerance. This offers a way to extend existing MBQC patterns to secret sharing protocols. Our characterisation of pointless measurements is believed also to be a useful tool for further integrated measurement based schemes, for example in constructing fault tolerant MBQC schemes.

References in corpus (7)

• Multi-party entanglement in graph states
• Graph States for Quantum Secret Sharing
• Determinism in the one-way model
• Generalized Flow and Determinism in Measurement-based Quantum Computation
• Parallelizing Quantum Circuits
• Finding Optimal Flows Efficiently
• Phase map decompositions for unitaries

Cited by in corpus (16)

• Quantum secret sharing with qudit graph states
• Experimentally Feasible Security Check for n-qubit Quantum Secret Sharing
• Non-Threshold Quantum Secret Sharing Schemes in the Graph State Formalism
• On the equivalence between sharing quantum and classical secrets, and error correction
• Which graph states are useful for quantum information processing?
• Graph States, Pivot Minor, and Universality of (X,Z)-measurements
• New Protocols and Lower Bound for Quantum Secret Sharing with Graph States
• 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
• Quantum linear network coding as one-way quantum computation
• Classical versus Quantum Graph-based Secret Sharing
• Reversibility in the Extended Measurement-based Quantum Computation
• Fragile entanglement statistics
• Algebraic characterisation of one-way patterns
• Inserting Planar-Measured Qubits into MBQC Patterns while Preserving Flow
• Qudit Clauser-Horne-Shimony-Holt Inequality and Nonlocality from Wigner Negativity