发表机构
Hefei Normal University; Anhui University（合肥师范学院; 安徽大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文完整分类了两个 qutrit 混合态在 LOCC 下的可逆转换，证明可逆转换等价于唯一最小纠缠块的局域酉等价，并给出负部分转置态的最小块求解方法。
AI 中文摘要
假设 Alice 和 Bob 可以通过局域操作和经典通信将一个共享的混合态变换为另一个，并且也能从第二个态恢复出第一个态。在这样的转换中，什么可以改变？我们给出了两个 qutrit 态之间可逆转换的完整分类。我们考虑单份拷贝的精确确定性 LOCC 变换，允许有限协议以及此处指定的可数协议。已知局域标记允许将可分离部分替换为局域制备，同时保留纠缠块。我们证明，对于两个相互可转换但不局域酉等价的纠缠态，这样的分解是必要的。这两个部分可以通过局域测量来区分。纠缠块具有相同的权重，并且在归一化后局域酉等价。每个纠缠态都有一个唯一的最小保留块。两个纠缠态可逆转换当且仅当这些未归一化的块局域酉等价。对于具有负部分转置的态，可以使用其部分转置的负特征空间以及至多三个矩阵零测试来找到最小块。
英文摘要
Suppose Alice and Bob can transform one shared mixed state into another by local operations and classical communication, and can also recover the first state from the second. What can change in such a conversion? We give a complete classification of reversible conversions between two-qutrit states. We consider exact deterministic LOCC transformations of a single copy, allowing finite protocols and the countable protocols specified here. Local flags are known to allow a separable part to be replaced by local preparation while an entangled block is retained. We prove that such a decomposition is necessary for two mutually convertible entangled states that are not locally unitarily equivalent. The two parts are distinguishable by local measurements. The entangled blocks have the same weight and are locally unitarily equivalent after normalization. Each entangled state has a unique smallest retained block. Two entangled states are reversibly convertible if and only if these unnormalized blocks are locally unitarily equivalent. For a state with negative partial transpose, the smallest block can be found using the negative eigenspace of its partial transpose and at most three matrix zero tests.
Comments22 pages, Comments and collaboration are welcome
