Approximate reconstructability of quantum states and noisy quantum secret sharing schemes

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.

arXiv comment6 pages, 1 figure

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Cited by in corpus (6)

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• Verifying the security of a continuous variable quantum communication protocol via quantum metrology
• Fundamental limits on quantum cloning from the no-signalling principle
• Recovery With Incomplete Knowledge: Fundamental Bounds on Real-Time Quantum Memories