AI 中文总结
该研究将范畴量子力学的量子信息流概念应用于全息框架，证明其轨迹满足比特线的约束，解释了比特线非唯一性的自然性，并通过ZX弦图发现QIF轨迹可探测更精细的纠缠结构。
AI 中文摘要
比特线作为全息纠缠熵极小曲面公式的凸对偶，是具有非平凡体轨迹的线状结构，其物理图像长期与贝尔对解释相关联，但其详细轨迹（尤其是非唯一性）的含义仍不明确。我们提出将范畴量子力学中发展的、适用于协议网络几何的Coecke量子信息流（QIF）概念应用于全息框架，证明其在离散全息体（即张量网络）内的轨迹满足比特线的无散度和密度约束条件。从这种以过程为中心的视角看，比特线的非唯一性变得自然：对于给定的资源态，实现同一蒸馏任务的不同协议可产生不同的QIF轨迹。我们进一步使用ZX弦图分析稳定子型全息张量网络，证明QIF轨迹可探测超出纠缠熵所捕获层次的更精细纠缠结构。
英文摘要
Bit threads, arising as the convex dual of the minimal-surface formula for holographic entanglement entropy, are line-like structures with nontrivial bulk trajectories. Their physical picture has long been associated with Bell-pair interpretations, yet the meaning of their detailed trajectories, particularly their nonuniqueness, remains unclear. We propose to apply Coecke's notion of quantum information flow (QIF) in protocol-network geometry, developed within categorical quantum mechanics, to a holographic setup, and show that its trajectories within the discrete holographic bulk---the tensor network---obey the divergence-free and density-bound conditions of bit threads. From this process-centered perspective, bit-thread nonuniqueness becomes natural: for a given resource state, different protocols realizing the same distillation task can give rise to different QIF trajectories. We further analyze stabilizer-type holographic tensor networks using ZX string diagrams and show that QIF trajectories can probe finer entanglement structure beyond the level captured by entanglement entropy.
Comments20 pages, 16 figures
