Concatenating Extended CSS Codes for Communication Efficient Quantum Secret Sharing

Recently, a class of quantum secret sharing schemes called communication efficient quantum threshold secret sharing schemes (CE-QTS) was introduced. These schemes reduced the quantum communication cost during secret recovery in quantum threshold secret sharing schemes. However, non-threshold schemes are known to have less storage cost compared to threshold schemes. This motivates us to extend the idea of communication efficiency to non-threshold schemes as well. 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. Specifically, we provide a framework for constructing CE-QSS schemes by concatenating a pair of CSS codes. The main component in this framework is a new class of Calderbank-Shor-Steane (CSS) codes called the extended CSS codes.