$(t, n)$ Threshold $d$-level quantum secret sharing based on quantum Fourier transformation

TL;DR

This paper introduces a new $(t, n)$ threshold quantum secret sharing scheme for sharing $d$-dimensional classical secrets, utilizing quantum Fourier transformation, local operations, and classical communication, with security against eavesdropping.

Contribution

It proposes a novel $(t, n)$ threshold QSS scheme for $d$-dimensional secrets, addressing previous scheme loopholes and ensuring security with local operations.

Findings

Scheme supports $d$-dimensional classical secrets.

Security is maintained against outsider and participant eavesdropping.

Implementation relies on local quantum operations and classical communication.

Abstract

Quantum secret sharing (QSS) is an important branch of secure multiparty quantum computation. Several schemes for $(n, n)$ threshold QSS based on quantum Fourier transformation (QFT) have been proposed. Inspired by the flexibility of $(t, n)$ threshold schemes, Song {\it et al.} (Scientific Reports, 2017) have proposed a $(t, n)$ threshold QSS utilizing $QFT$. Later, Kao and Hwang (arXiv:1803.00216) have identified a loophole in the scheme but have not suggested any remedy. In this present study, we have proposed a $(t, n)$ threshold QSS scheme to share a $d$ dimensional classical secret. This scheme can be implemented using local operations (such as $QFT$, generalized Pauli operators and local measurement) and classical communication. Security of the proposed scheme is described against outsider and participants' eavesdropping.