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Equivalence between sharing quantum and classical secrets and error correction

机译:共享量子和经典机密以及纠错之间的对等

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摘要

We present a general scheme for sharing quantum secrets, and an extension to sharing classical secrets, which contain all known quantum-secret-sharing schemes. In this framework, we show the equivalence of existence of both schemes, that is, the existence of a scheme sharing a quantum secret implies that the extended classical-secret-sharing scheme works, and vice versa. As a consequence of this, we find schemes sharing classical secrets for arbitrary access structures. We then clarify the relationship to quantum error correction and observe several restrictions thereby imposed, which for example indicates that for pure-state threshold schemes the share size q must scale with the number of players n as q≥√n. These results also provide a way of searching for quantum-error-correcting codes.
机译:我们提出了一个共享量子秘密的通用方案,并扩展了共享经典秘密的扩展,其中包含了所有已知的量子秘密共享方案。在此框架中,我们证明了这两种方案都存在相同,即,存在一个共享量子秘密的方案意味着存在扩展的经典秘密共享方案,反之亦然。结果,我们发现了针对任意访问结构共享经典机密的方案。然后,我们阐明与量子误差校正的关系,并观察到由此施加的若干限制,例如,这表明对于纯状态阈值方案,份额大小q必须随着参与者数量n≥q≥√n进行缩放。这些结果还提供了一种搜索量子纠错码的方法。

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