AI 中文总结
研究量子信息编码到n个物理载体中，擦除部分载体后恢复信息的概率问题，通过建立新的不可克隆约束，证明了M.B. Hastings关于载体擦除概率t≥1/2时的恢复猜想。
AI 中文摘要
假设我们将量子信息编码到n个物理载体中。在一些载体组被擦除后，我们能以多大的概率完美恢复量子信息？这个问题出现在量子擦除信道的研究中，M.B. Hastings猜想，如果每个载体以概率t≥1/2独立擦除，那么不可能以渐近消失的误差和概率>1 - t恢复量子信息。我们通过建立关于可实现恢复概率的新的不可克隆约束来证明这个猜想。
英文摘要
Suppose that we encode quantum information into $ n $ physical carriers. With what probabilities can we perfectly recover the quantum information after sets of carriers have been erased? This question arises in the study of quantum erasure channels, for which M.B. Hastings conjectured that if each carrier is independently erased with probability $ t \geq 1/2 $, then it is impossible to recover the quantum information with asymptotically vanishing error and probability $ > 1-t $. We prove this conjecture by establishing new no-cloning constraints on realizable recovery probabilities.
Comments5.55 pages, 6.15 pages of supplemental material, 3 figures. See arXiv:2607.08591 for an independent proof of the erasure-simulation conjecture. The manuscript has been edited further for clarity and consistency
