Approximate reconstructability of quantum states and noisy quantum secret sharing schemes

• URL: http://arxiv.org/abs/2302.02509v2
• Date: Tue, 15 Aug 2023 21:33:53 GMT
• Title: Approximate reconstructability of quantum states and noisy quantum secret sharing schemes
• Authors: Yingkai Ouyang, Kaumudibikash Goswami, Jacquiline Romero, Barry C. Sanders, Min-Hsiu Hsieh and Marco Tomamichel
• Abstract summary: We analyse approximate quantum secret sharing in a formal cryptographic setting. In particular, we show that approximate reconstructability of the quantum secret by these players is possible if and only if the information leakage is small.
• Score: 19.170626575317907
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce and analyse approximate quantum secret sharing in a formal cryptographic setting, wherein a dealer encodes and distributes a quantum secret to players such that authorized structures (sets of subsets of players) can approximately reconstruct the quantum secret and omnipotent adversarial agents controlling non-authorized subsets of players are approximately denied the quantum secret. In particular, viewing the map encoding the quantum secret to shares for players in an authorized structure as a quantum channel, we show that approximate reconstructability of the quantum secret by these players is possible if and only if the information leakage, given in terms of a certain entanglement-assisted capacity of the complementary quantum channel to the players outside the structure and the environment, is small.

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