AI 中文总结
本文证明了无需通信即可局域化的二分秩一理想测量等价于在等维块上复制单个尼斯-贝尔基，证实了Akibue和Miyazaki的猜想1。
AI 中文摘要
我们证明了有限维二分秩一理想投影测量的完整结构刻画，这些测量在Akibue和Miyazaki的意义下无需通信即可局域化。在局域酉等价下，每个这样的测量基是通过在等维局域子空间块上复制单个尼斯-贝尔基而获得的。必要性证明结合了Beckman、Gottesman、Nielsen和Preskill建立的完全测量的因果块结构，以及他们关于可局域化超算子的本征态合成定理。首先迫使一个参考块成为尼斯-贝尔基；然后同一定理将该基一致地传播到每一行、每一列和内部块。充分性由Akibue和Miyazaki的显式局域化协议得出。这证实了他们的猜想1，并给出了该设置中二分秩一理想测量的协议无关分类。
英文摘要
We prove a complete structural characterization of finite-dimensional bipartite rank-one ideal projective measurements that are localizable without communication in the sense of Akibue and Miyazaki. Up to local-unitary equivalence, every such measurement basis is obtained by replicating a single nice Bell basis across equal-dimensional local subspace blocks. The necessity proof combines the causal block structure of complete measurements established by Beckman, Gottesman, Nielsen, and Preskill with their eigenstate-composition theorem for localizable superoperators. A reference block is first forced to be a nice Bell basis; the same theorem then propagates that basis consistently along every row, column, and interior block. The converse follows from the explicit localization protocol of Akibue and Miyazaki. This establishes their Conjecture 1 and gives a protocol-independent classification of bipartite rank-one ideal measurements in this setting.
Comments3 pages. Proves Conjecture 1 of Akibue and Miyazaki, Phys. Rev. A 113, 052430 (2026), arXiv:2601.02660v2
