High-efficient quantum secret sharing based on the Chinese remainder theorem via the orbital angular momentum entanglement analysis

Abstract

We investigate a novel quantum secret sharing (QSS) based on the Chinese remainder theory (CRT) in multi-dimensional Hilbert space with the orbital angular momentum (OAM) entanglement analysis. The secret is divided and then allotted to two or more participants who prepare pairs of photons in the OAM-entanglement states. The initial secret can be restored jointly by legal participants via the OAM-entanglement analysis on the corresponding photons. Its security is guaranteed from the OAM entanglement of photons that are established through the spin angular momentum (SAM) entanglement analysis performed on the generated SAM-based OAM hybrid entanglement photons. It provides an alternative technique for the QSS while producing the OAM entanglement photons in the combined multi-dimensional OAM Hilbert space, where the CRT is conducted properly for sharing the conventional secret among legal participants.

Quantum secret sharing by using Fourier transform on orbital angular momentum

“…Guo and Zhao [31] used the Chinese remainder theory and the OAM in multi‐dimensional Hilbert space to propose another QSS scheme. Guo's scheme needs the OAM entangled state, and the generation of the OAM entangled state is very complicated, that is, the dealer generates the spin angular momentum (SAM) and OAM hybrid‐entanglement state, and then performs the entanglement measurement on SAM to generate the OAM entangled state.…”

Multiparty weighted threshold quantum secret sharing based on the Chinese remainder theorem to share quantum information

“…Quantum secret sharing (QSS) has been developed firstly by Hillery et al 8 in 1999, they built QSS with Greenberger-Horne-Zeilinger (GHZ) states, which inspired numerous studies afterward 9 , 10 . However, most studies use traditional methods such as Lagrange Interpolation to build quantum secret sharing schemes, which focuses on the distribution of classical bits as shares 11 , 12 instead of sharing quantum bits. Hence, this study focus on sharing the quantum information with Chinese Remainder Theorem (CRT), because CRT can use different coprime divisors as the respective weight of the agents (unlike Lagrange Interpolation).…”

“…Quantum secret sharing is more difficult than with classical information. Thus, most proposed schemes for sharing secrets use classical information 10 – 12 not quantum information 13 – 16 . Moreover, -weighted threshold quantum secret sharing scheme are more difficult both than ( n , n )-quantum secret sharing and ( t , n )-threshold quantum secret sharing schemes.…”

Continuous Variable Quantum Secret Sharing with Fairness

“…Hence, compared with other protocols, such as quantum key distribution [5][6][7], quantum signature [8], Quantum anonymous voting [9] and so on, the QSS protocols need to analysis the attack from both inside and outside. But in the previous literatures, it is rarely discussed how the secret is revealed securely against inner attack [10][11][12][13]. Until now, many SS protocols have been improved to verify participants and check the validity of shares in the recovery phase [14][15][16], but the participant who is the last one to release share, would desire to obtain the secret alone by sending fake share or keeping silence.…”