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

TL;DR

This paper develops multi-level quantum secret sharing schemes using mutually unbiased and biased bases, achieving high security and efficiency, and introduces protocols to enhance security against various attacks.

Contribution

It presents general multi-partite quantum secret sharing schemes with simple measurement conditions and proposes new protocols combining quantum key distribution for improved security.

Findings

High-dimensional mutually unbiased bases enable near-perfect security.

Mutually biased bases achieve optimal non-perfect security at 4-level systems.

New protocols enhance security and efficiency against entanglement-assisted attacks.

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.