Quantum Secret Sharing with Multi-level Mutually (Un-)Biased Bases

Abstract

We construct general schemes for multi-partite quantum secret sharing using multi-level systems, and find that the consistent conditions for valid measurements can be summarized in two simple algebraic conditions. The scheme using the very high dimensional mutually unbiased bases can in principle achieve perfect security against intercept-resend attack; and for the scheme using mutually biased bases, it reaches the optimal but non-perfect security at 4-level system. We also address the security issue against the general attacks in the context of our multi-level schemes. Especially, we propose new protocol to enhance both the efficiency and the security against the entanglement-assisted participant's attack by incorporating quantum-key-distribution and measurement-basis-encrypted schemes so that its security is as robust as quantum-key-distribution.

arXiv comment5 pages, v2 typos corrected, v3 content improved, v4 propose a new protocol against entanglement-assisted participant's attack

References in corpus (6)

• Quantum secret sharing
• How to share a quantum secret
• Security of quantum key distribution using d-level systems
• Efficient Multi-Party Quantum Secret Sharing Schemes
• Quantum cryptography with 3-state systems
• Cryptanalysis of the Hillery-Buzek-Berthiaume quantum secret-sharing protocol

Cited by in corpus (29)

• Higher-dimensional orbital angular momentum based quantum key distribution with mutually unbiased bases
• Entanglement detection via mutually unbiased bases
• Secret Sharing with a Single d-level Quantum System
• Four-photon orbital angular momentum entanglement
• Mutually unbiased bases and symmetric informationally complete measurements in Bell experiments
• Quantum Secret Sharing and Random Hopping; Using single states instead of entanglement
• Experimental quantum secret sharing with spin-orbit structured photons
• Experimental Demonstration of Sequential Multiparty Quantum Secret Sharing and Quantum Conference Key Agreement
• Unextendible maximally entangled bases and mutually unbiased bases
• Generalized Pauli channels and a class of non-Markovian quantum evolution
• Entanglement witnesses from mutually unbiased bases
• A verifiable framework of entanglement-free quantum secret sharing with information-theoretical security
• Verifiable Threshold Quantum Secret Sharing with Sequential Communication
• A Note on Mutually Unbiased Unextendible Maximally Entangled Bases in ${\mathbb{C}}^2⨂{\mathbb{C}}^3$
• Fine-grained uncertainty relations for several quantum measurements
• The Magical Number Seven: An Unexpected Dimensional Threshold in Quantum Communication Complexity
• Experimental Efficient Source-Independent Quantum Secret Sharing against Coherent Attacks
• Source-independent quantum secret sharing with entangled photon pair networks
• Eavesdropping on the improved three-party quantum secret sharing protocol
• Differential Phase Shift Quantum Secret Sharing Using a Twin Field with Asymmetric Source Intensities
• Orbits of mutually unbiased bases
• States that "look the same" with respect to every basis in a mutually unbiased set
• Structure of the sets of mutually unbiased bases with cyclic symmetry
• Novel Constructions of Mutually Unbiased Tripartite Absolutely Maximally Entangled Bases
• Mutually disjoint, maximally commuting set of physical observables for optimum state determination
• A secret sharing scheme on p^2 -dimensional quantum system
• Quantum Access Structure and Secret Sharing
• Sharing a quantum secret without a trusted party
• Designing generalized elegant Bell inequalities in higher dimensions from a Tsirelson bound