发表机构
School of Mathematics, South China University of Technology; School of Computer Science and Technology, Dongguan University of Technology（华南理工大学数学学院; 东莞理工学院计算机科学与技术学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究多副本量子态判别中集体局域测量的能力，证明集体处理可降低奇素数维最大稳定子基的副本复杂度至三，但一般情形下多副本困难性依然存在，揭示三种资源的不同作用。
AI 中文摘要
二十多年前，Bennett等人[Phys. Rev. A 59, 1070 (1999)]提出了一个问题：完美局域判别正交量子态是否可能需要多于两个副本。这个问题随后针对分别处理各副本的自适应协议得到了解答[Phys. Rev. Lett. 126, 210505 (2021)]，但当每个实验室被允许集体处理其局域副本时，该问题仍然悬而未决。在此，我们解决了这一更强的设定，并将跨重复局域输入的集体访问识别为一种独特的资源。对于每个固定的奇素数局域维度，存在完备的最大稳定子本征基，其基于单副本可分离测量的副本复杂度随系统规模发散。在集体处理下，这种行为发生急剧变化：在奇素数局域维度中，每个最大稳定子本征基都可以通过一轮集体LOCC使用至多三个副本被完美解码。然而，集体处理通常并不能消除多副本的困难性。对于每个固定的局域维度d≥2，我们证明在一个显式的相位族内，存在完备基，其副本复杂度即使在集体可分离测量下仍然无界，并以子系统数量的平方根作为下界尺度。因此，样本数量、空间测量能力和跨重复局域输入的相干访问是分布式量子测量中不同的资源。
英文摘要
More than two decades ago, Bennett \emph{et al.} [Phys. Rev. A \textbf{59}, 1070 (1999)] asked whether perfect local discrimination of orthogonal quantum states can require more than two copies. This question was subsequently answered for adaptive protocols that process the copies separately [Phys. Rev. Lett. \textbf{126}, 210505 (2021)], but remained open when each laboratory is allowed to process its local copies collectively. Here we resolve this stronger setting and identify collective access across repeated local inputs as a distinct resource. For every fixed odd-prime local dimension, there exist complete maximal-stabilizer eigenbases whose copy complexity under individual-copy separable measurements diverges with system size. Under collective processing this behavior changes sharply: every maximal-stabilizer eigenbasis in odd-prime local dimension is perfectly decoded by one-round collective LOCC using at most three copies. Collective processing, however, does not remove multicopy hardness in general. For every fixed local dimension $d\ge2$, we prove the existence, within an explicit phase family, of complete bases whose copy complexity remains unbounded even under collective separable measurements, with a square root of the number of subsystems as lower-bound scale. Thus sample number, spatial measurement power, and coherent access across repeated local inputs are distinct resources in distributed quantum measurement.
Comments7+23 pages, 1 figure
