Concatenating Extended CSS Codes for Communication Efficient Quantum Secret Sharing

TL;DR

This paper introduces a broad class of communication efficient quantum secret sharing schemes, generalizing previous threshold schemes, by utilizing extended CSS codes to reduce communication costs during secret recovery.

Contribution

It proposes a new framework for constructing CE-QSS schemes using extended CSS codes, encompassing both threshold and non-threshold schemes, and establishes bounds on communication costs.

Findings

Derived a lower bound on communication cost for CE-QSS schemes.

Constructed CE-QSS schemes that meet the derived bound.

Generalized earlier threshold schemes to include non-threshold schemes.

Abstract

Recently, a class of quantum secret sharing schemes called communication efficient quantum threshold secret sharing schemes (CE-QTS) was introduced. These schemes reduced the communication cost during secret recovery. In this paper, we introduce a general class of communication efficient quantum secret sharing schemes (CE-QSS) which include both threshold and non-threshold schemes. We propose a framework for constructing CE-QSS schemes to generalize the earlier construction of CE-QTS schemes which was based on the staircase codes. The main component in this framework is a class of quantum codes which we call the extended Calderbank-Shor-Steane codes. These extended CSS codes could have other applications. We derive a bound on communication cost for CE-QSS schemes. Finally, we provide a construction of CE-QSS schemes meeting this bound using the proposed framework.