发表机构
Central High School; Department of Mathematics, University of Illinois at Urbana-Champaign; Department of Physics, University of Rhode Island（中央高中; 伊利诺伊大学厄巴纳-香槟分校数学系; 罗德岛大学物理系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究解决了多部分Werner态量子数据隐藏的最优安全界问题，证明区分偏差为O(n^2/d)，并将认证隐藏范围从n=O(d^{1/4})扩展到n=O(√d)，同时展示了表示论方法在量子性质测试中的价值。
AI 中文摘要
量子数据隐藏关注的是这样一对状态：它们在全局测量下高度可区分，但在限制为局域操作和经典通信时几乎不可区分。在Eggeling和Werner引入基于Werner态的多部分隐藏方案二十多年后，其均匀安全保证对参与方数量和局域维度的最优依赖关系仍然未知。我们通过证明任意一对$n$-qudit Werner态在测量效应在每一二分部下对部分转置（PPT）保持正性的测量下的区分偏差为$O(n^2/d)$来解决这个问题。一个显式的状态对仅使用非自适应局域测量即可达到该缩放，确立了最坏情况下的最优性，并表明PPT松弛保留了参与方数量和局域维度两者的最优依赖关系。在固定安全性下，这将认证隐藏区域从$n=O(d^{1/4})$扩展到$n=O(\sqrt d)$。在数据隐藏之外，同样的界意味着使用自适应单拷贝测量测试任何非平凡的酉不变性质需要$\Omega(\sqrt d)$个拷贝，从而为任何在集体测量下具有维度无关样本复杂度的性质产生分离。我们的证明将区分偏差归结为部分转置算子的迹范数，并使用混合Schur-Weyl对偶性对其进行分析，展示了为基于端口隐形传态开发的表示论方法在数据隐藏和量子性质测试中的实用性。
英文摘要
Quantum data hiding concerns pairs of states which are highly distinguishable with global measurements, yet nearly indistinguishable when restricted to local operations and classical communication. More than two decades after Eggeling and Werner introduced a multipartite hiding scheme based on Werner states, the optimal dependence of its uniform security guarantee on the number of parties and local dimension remained unknown. We resolve this problem by showing that the distinguishing bias of any pair of $n$-qudit Werner states is $O(n^2/d)$ under measurements whose effects remain positive under partial transposition (PPT) across every bipartition. An explicit pair attains this scaling using only nonadaptive local measurements, establishing worst-case optimality and showing that the PPT relaxation preserves the optimal dependence on both the number of parties and the local dimension. At fixed security, this extends the certified hiding regime from $n=O(d^{1/4})$ to $n=O(\sqrt d)$. Beyond data hiding, the same bound implies that testing any nontrivial unitarily invariant property with adaptive single-copy measurements requires $Ω(\sqrt d)$ copies, yielding separations for any property with dimension-independent sample complexity under collective measurements. Our proof reduces the distinguishing bias to trace norms of partially transposed operators and analyzes them using mixed Schur-Weyl duality, demonstrating the utility of representation theoretic methods developed for port-based teleportation to data hiding and quantum property testing.
