A secret sharing scheme on p^2 -dimensional quantum system

TL;DR

This paper develops a quantum secret sharing scheme on p^2-dimensional systems using mutually unbiased bases, offering enhanced scalability and security analysis for single-qudit protocols.

Contribution

It introduces a new secret sharing scheme on p^2-dimensional quantum systems utilizing mutually unbiased bases and unitary transformations, improving scalability over existing methods.

Findings

Constructed mutually unbiased bases for p^2-dimensional systems

Developed a (N,N) threshold secret sharing protocol

Analyzed security against various quantum attacks

Abstract

In this paper, we give the mutually unbiased bases on the p^2 -dimensional quantum system where p is an odd prime number, and construct the corresponding unitary transformation based on the properties of these mutually unbiased bases. Then, we construct a (N,N) threshold secret sharing scheme using unitary transformation between these mutually unbiased bases, and analyze the scheme's security by several ways, for example, intercept-and-resend attack, entangle-and-measure attack, Trojan horse attack, and so on. Using our method, we construct a single-particle quantum protocol involving only one qudit, and the method shows much more scalability than other schemes.