AI 中文总结
该研究确立了多体纠缠相较无预共享纠缠的量子通信的指数优势，构造了双源随机数提取器，在受限存储密码学中实现了纠缠与无纠缠量子侧信息的指数分离。
AI 中文摘要
我们确立了多体量子纠缠所实现的指数通信优势。基于两方隐藏匹配问题，我们提出了一个涉及多个空间分离发送方和单个接收方的通信任务。我们证明，共享的Greenberger-Horne-Zeilinger（GHZ）态可让每个发送方仅使用对数量级的经典通信完成该任务。相比之下，若没有预共享纠缠，即使允许量子通信，任何能达到高成功概率的协议都至少需要一个发送方进行多项式量级的通信。因此，受多体纠缠辅助的经典通信，比无预共享纠缠的量子通信具有指数级的能力优势。作为密码学应用，我们构造了一个带种子的双源随机数提取器，并确立了纠缠与无纠缠量子侧信息之间的指数分离。具体而言，破解该提取器需要两个分别存储两个源信息的无纠缠量子态，这需要多项式规模的内存，而在存在少量预共享纠缠的情况下，仅需指数级更小的量子内存即可完成。
英文摘要
We establish an exponential communication advantage enabled by multipartite quantum entanglement. Building on the bipartite Hidden Matching problem, we introduce a communication task involving multiple spatially separated senders and a single receiver. We show that a shared Greenberger-Horne-Zeilinger state enables completion of this task using only logarithmically many bits of classical communication from each sender. In contrast, without preshared entanglement, any protocol achieving high success probability requires polynomial communication from at least one sender, even when \emph{quantum} communication is allowed. Thus, classical communication assisted by multipartite entanglement can be exponentially more powerful than quantum communication without preshared entanglement. As a cryptographic application, we construct a seeded two-source randomness extractor and establish an exponential separation between entangled and unentangled quantum side-information. Specifically, compromising the extractor with two unentangled quantum states storing information about the two sources, respectively, requires polynomial-size memory, whereas exponentially smaller quantum memory suffices in the presence of a small amount of shared entanglement.
Comments5.25 pages (double-column) + 3.5 pages (single-column); 2 figures; Comments are welcome
