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arXiv:2512.09699

Device Independent Quantum Secret Sharing Using Multiparty Pseudo-telepathy Game

Santanu Majhi, Goutam Paul

quant-phcs.CRSubmitted Dec 10, 2025• Announced Dec 11, 2025• 0 citations
v1 · Dec 10, 2025v2 · Jan 2, 2026
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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.

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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.
Device-independent conference key agreement (DI-CKA) lets a group of parties establish a shared secret key from untrusted quantum devices, with security certified by non-locality. Existing DI-CKA protocols are each built around a single Bell inequality, typically a multiparty variant of the CHSH game. DI-QKD protocols, in contrast, have been built from a much richer landscape of non-local games, and it has remained unclear how to carry this landscape over to the conference setting. We introduce $\textit{Parity-$G$ games}$, which extend any two-player game GGG to NNN players, for every NNN, provided GGG has an optimal strategy in which one player measures Pauli observables. The extension preserves the quantum and classical values of GGG, and the security of the resulting NNN-party protocol follows from an analysis of the two-player game alone. Our framework recovers the Parity-CHSH game of Ribeiro, Murta and Wehner (Phys. Rev. A, 2018) as a special case. Applied to the Mermin--Peres Magic Square Game, it yields a new NNN-player pseudo-telepathy game, the Parity Magic Square Game\textit{Parity Magic Square Game}Parity Magic Square Game, which ideal devices win in every round. We use it to construct the first\textit{first}first DI-CKA protocol based on a pseudo-telepathy game. We prove the protocol secure against coherent attacks. It produces up to two key bits per round, and at low noise its key rate exceeds that of the DI-CKA protocol based on the Parity-CHSH game.
Quantum secret sharing (QSS) enables a dealer to securely distribute keys to multiple players. Device-independent (DI) QSS can resist all possible attacks from practical imperfect devices and provide QSS the highest level of security in theory. However, DI QSS requires high-performance devices, especially for low-noise channels, which is a big challenge to demonstrate experimentally. We propose a DI QSS protocol with the advanced random key generation basis strategy, which combines the random key generation basis with the noise preprocessing and postselection strategies. We develop the methods to numerically simulate the key generation rate in an acceptable time. Our DI QSS protocol has some advantages. First, it can increase the noise tolerance threshold from an initial 7.147% to 9.231% (29.16% growth) and reduce the global detection efficiency threshold from 96.32% to 93.41%. The maximal distance between any two users increases to 1.43 km, which is about 5.5 times the initial value. Second, by randomly selecting two basis combinations to generate the key, our DI QSS protocol can reduce the entanglement resource consumption. Our protocol has potential for the experimental demonstration of DI QSS and application in the future.
Device-independent quantum key distribution (DIQKD) is information-theoretically secure against adversaries who possess a scalable quantum computer and who have supplied malicious key-establishment systems; however, the DIQKD key rate is currently too low. Consequently, we devise a DIQKD scheme based on the quantum nonlocal Mermin-Peres magic square game: our scheme asymptotically delivers DIQKD against collective attacks, even with noise. Our scheme outperforms DIQKD using the Clauser-Horne-Shimony-Holt game with respect to the number of game rounds, albeit not number of entangled pairs, provided that both state visibility and detection efficiency are high enough.
Abstract Quantum secret sharing (QSS) stands as one of the most promising components of quantum cryptography. Device-independent quantum secret sharing (DI-QSS) provides enhanced security by eliminating the need for device trust, yet its practical performance remains constrained by channel loss and noise. To overcome this limitation, this work innovatively integrates tripartite advantage distillation (AD) with an advanced random key generation basis strategy. This approach effectively improves the protocol’ s noise tolerance, reduces the global detection effciency threshold, and significantly extends the maximum secure communication distance. Numerical simulations demonstrate that, under ideal noisy channel conditions, the protocol’ s maximum secure distance increases from 0.82 km to 4.13 km, its global detection effciency threshold decreases from 93.42% to 80.23%, and the noise tolerance rises from 9.23% to 24.18%. This scheme significantly enhances the robustness of the protocol.
Device-independent quantum secret sharing (DI-QSS) provides high security by eliminating the need to trust devices, yet its practical performance is limited by channel loss and noise. This work extends advantage distillation from two-party quantum key distribution (QKD) to three-party DI-QSS, redesigning the corresponding data interaction and verification procedures. The technique is systematically applied to the basic protocol and three active improvement strategies: noise preprocessing, post-selection, and their combination. This approach enhances noise tolerance, reduces the required global detection efficiency threshold, and significantly extends the maximum secure communication distance. Numerical simulations demonstrate that for the basic protocol over fiber, the maximum secure distance increases from 0.16 km to 1.85 km, and the noise tolerance improves from 10.17% to 28.49%. The results show that generalizing advantage distillation to the three-party setting effectively strengthens the protocol's robustness and practicality, enhancing its adaptability to realistic noise and advancing the development of more reliable quantum secret sharing systems.
Device-independent quantum secret sharing (DI QSS) relaxes security assumptions of experimental devices to provide the highest security level for QSS. Previous DI QSS protocols require to generate multi-partite entangled states and then implement the long-distance entanglement distribution. The extremely low generation probability of current multi-partite entanglement source and photon transmission loss largely limit DI QSS's practical key generation rate and secure photon transmission distance. In the paper, we propose a high-efficient long-distance DI QSS protocol based on practical nearly on-demand single-photon sources (SPSs), which adopts the single photons and heralded architecture to construct long-distance multi-partite entanglement channels. Our SPS DI QSS protocol can automatically eliminate the negative influence from photon transmission loss and largely increase the secure photon transmission distance. Moreover, we adopt active improvement strategies such as random key generation basis, postselection, and advanced postselection to further increase the practical key generation rate and lower the experimental requirement. Comparing with previous DI QSS protocols based on entanglement sources, our SPS DI QSS protocol can increase the practical communication efficiency by six orders of magnitude, and increase the secure photon transmission distance by at least 151 times. This SPS DI QSS protocol is feasible with the current experimental technologies. Our protocol makes it possible to realize high-efficient long-distance DI network in the near future.