Device Independent Quantum Secret Sharing Using Multiparty Pseudo-telepathy Game

TL;DR

This work presents the first DI-QSS protocol based on a pseudo-telepathy parity game without requiring dedicated rounds and specific basis configuration, unlike CHSH-based DI-QSS schemes, and shows a bitwise advantage over the previous protocol for producing the same raw key length.

Abstract

Device-independent quantum secret sharing (DI-QSS) is a cryptographic protocol that overcomes the security limitations posed by untrusted quantum devices. We propose a DI-QSS protocol based on the multipartite pseudo-telepathy parity game, which achieves device-independence with simultaneous key generation without requiring dedicated test rounds, unlike CHSH-based schemes [Zhang et al., Phys. Rev. A, 2024]. Notably, the proposed scheme allows simultaneous device-independence verification and key-generation phases, achieving optimal performance for a seven-qubit GHZ state configuration. Further, we analyse the security of our protocol against collective attack and establish reduced resource requirement for the same length of the raw key compared to the previous protocol. Finally, we show that our protocol remains robust even in a noisy environment.

Figures (3)

• Figure I: Relationships of three users’ measurement results. Alice’s measurement bases are shown in the first row, Bob’s measurement bases are shown in the first column, and Charlie’s measurement results appear in the boxes.
• Figure II: Multiparty pseudotelepathy game
• Figure III: Variation of the ratio with the number of parties $n$. For $n = 3$, the ratio is $0.25$. For $n = 4$, the ratio remains $0.25$. For $n = 5$, the ratio increases to $0.375$. For $n = 6$, it further rises to $0.5$. For $n = 7$, the ratio reaches $0.5625$, and it remains the same for $n = 8$. For $n = 9$, the ratio slightly decreases to $0.53125$, and for $n = 10$, it returns to $0.5$.

Theorems & Definitions (3)

• proof
• proof
• proof