Reducing the quantum communication cost of quantum secret sharing

TL;DR

This paper introduces a novel quantum secret sharing scheme that reduces quantum communication costs by combining imperfect quantum and classical secret sharing, enabling smaller quantum components and more efficient protocols.

Contribution

The authors present a new construction for perfect quantum secret sharing that uses imperfect ramp schemes with classical encryption, achieving lower quantum communication and share sizes.

Findings

Schemes can be performed with smaller quantum components.

Combining imperfect quantum and classical sharing yields perfect schemes.

Examples achieve minimal share sizes for given access structures.

Abstract

We demonstrate a new construction for perfect quantum secret sharing (QSS) schemes based on imperfect "ramp" secret sharing combined with classical encryption, in which the individual parties' shares are split into quantum and classical components, allowing the former to be of lower dimension than the secret itself. We show that such schemes can be performed with smaller quantum components and lower overall quantum communication than required for existing methods. We further demonstrate that one may combine both imperfect quantum and imperfect classical secret sharing to produce an overall perfect QSS scheme, and that examples of such scheme (which we construct) can have the smallest quantum and classical share components possible for their access structures, something provably not achievable using perfect underlying schemes. Our construction has significant potential for being adapted to other QSS schemes based on stabiliser codes.