论文标题
几乎完整的解决方案，解决了铃对角Qutrits的NP可分离性问题
Almost complete solution for the NP-hard separability problem of Bell diagonal qutrits
论文作者
论文摘要
由于$ 95 \％$的成功概率，我们解决了贝尔对角线QUTRIT状态的可分离性问题，该状态具有正面偏置（PPT）。可分离性问题，即区分可分离和纠缠状态，通常由于存在绑定的纠缠状态而缺乏有效的解决方案。与可通过本地操作和经典交流可用于纠缠蒸馏的自由纠缠状态相反，这些状态无法通过Peres-Horodecki标准或PPT标准来检测。我们分析了一个可以分离，自由纠缠或纠缠的一大批Qutrit状态。利用这些状态在欧几里得空间中的几何表示，提出了新的方法，可以有效地将可分离和结合的纠缠铃对角状态分类。此外，该分类允许精确确定可分离，自由和绑定纠缠状态类别的相对体积。详细介绍，在所有贝尔对角ppt中，$ 81.0 \％\％\ pm0.1 \％$ $ $ $ $ $ $ $ $ $ $ $ $ $ $ 13.9 \ pM0.1 \％$ $绑定为绑定，仅$ 5.1 \ pm0.1 \％$ $ $ \％$仍然未分类。此外，将我们的应用标准作为结合纠缠的检测器进行比较，该标准表明没有单个标准能够检测所有绑定的纠缠状态。
With a probability of success of $95 \%$ we solve the separability problem for Bell diagonal qutrit states with positive partial transposition (PPT). The separability problem, i.e. distinguishing separable and entangled states, generally lacks an efficient solution due to the existence of bound entangled states. In contrast to free entangled states that can be used for entanglement distillation via local operations and classical communication, these states cannot be detected by the Peres-Horodecki criterion or PPT criterion. We analyze a large family of bipartite qutrit states that can be separable, free entangled or bound entangled. Leveraging a geometrical representation of these states in Euclidean space, novel methods are presented that allow the classification of separable and bound entangled Bell diagonal states in an efficient way. Moreover, the classification allows the precise determination of relative volumes of the classes of separable, free and bound entangled states. In detail, out of all Bell diagonal PPT states $81.0 \%\pm0.1\%$ are determined to be separable while $13.9\pm0.1\%$ are bound entangled and only $5.1\pm0.1\%$ remain unclassified. Moreover, our applied criteria are compared for their effectiveness and relation as detectors of bound entanglement, which reveals that not a single criterion is capable to detect all bound entangled states.
