Concatenating Extended CSS Codes for Communication Efficient Quantum Secret Sharing

• URL: http://arxiv.org/abs/2211.06910v1
• Date: Sun, 13 Nov 2022 14:21:59 GMT
• Title: Concatenating Extended CSS Codes for Communication Efficient Quantum Secret Sharing
• Authors: Kaushik Senthoor and Pradeep Kiran Sarvepalli
• Abstract summary: Recently, a class of quantum secret sharing schemes called communication efficient quantum threshold secret sharing schemes (CE-QTS) was introduced. 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.
• Score: 3.8073142980733
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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