发表机构
Virginia Tech（弗吉尼亚理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该论文在黑尔随机预言机模型中证明从黑洞辐射恢复单量子比特的最优查询界，并应用于构造EFI对和量子承诺。
AI 中文摘要
我们在黑尔随机预言机模型中证明了从黑洞辐射中恢复单个量子比特的最优查询界，前提是剩余黑洞包含系统量子比特至多十六分之一。若恢复相对于平凡解码具有任何恒定的黑尔平均优势，则所需查询数正比于剩余黑洞的希尔伯特空间维度。下界对于独立于采样酉矩阵选择的解码器是无条件的，允许查询之间进行任意计算，并可访问 $U, U^dagger, U^*, U^\mathsf T$ 及其受控变体。一个仅使用正向和逆向查询的现有解码器达到了匹配的界。证明使用路径记录预言机来比较真实态和最大混合态。作为应用，我们获得了相对于公共黑尔预言机可高效制备、统计上远离、计算上不可区分的（EFI）对和量子承诺，并证明了固定目标族上乌尔曼变换的紧线性秩下界。
英文摘要
We prove optimal query bounds for recovering a single qubit from black-hole radiation in the Haar random oracle model, when the remaining black hole contains at most one sixteenth of the system's qubits. Recovery with any constant Haar-averaged advantage over trivial decoding requires queries proportional to the Hilbert-space dimension of the remaining black hole. The lower bound is unconditional for decoders chosen independently of the sampled unitary, allows arbitrary computation between queries, and access to $U, U^\dagger, U^*, U^\mathsf T$ along with the controlled variants. An existing decoder using only forward and inverse queries attains a matching bound. The proof uses a path recording oracle to compare real and maximally mixed states. As applications, we obtain an efficiently preparable, statistically far, computationally indistinguishable (EFI) pair and quantum commitments relative to a public Haar oracle, as well as prove a tight linear rank lower bound for Uhlmann transformation on a fixed-target family.
Comments67 pages, 4 figures
