Title:	Approximate reconstructability of quantum states and noisy quantum secret sharing schemes
Authors:	Ouyang, Yingkai Goswami, Kaumudibikash Romero, Jacquiline Sanders, Barry C. Hsieh, Min-Hsiu Tomamichel, Marco
Issue Date:	21-Jul-2023
Publisher:	American Physical Society
Citation:	Physical Review A, 2023, Vol.108, p012425
Abstract:	We introduce and analyze 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 nonauthorized subsets of players are approximately denied the quantum secret. In particular, viewing the map encoding the quantum secret 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.
Description:	Restricted Access
URI:	http://hdl.handle.net/2289/8272
Alternative Location:	https://arxiv.org/abs/2302.02509 http://dx.doi.org/10.1103/PhysRevA.108.012425 https://ui.adsabs.harvard.edu/abs/2023PhRvA.108a2425O/abstract
Copyright:	2023, American Physical Society
Appears in Collections:	Research Papers (TP)

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