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arXiv · 2608.19428

Holographic Bit Threads from String-Diagrammatic Quantum Information Flow

Yi-Yu Lin·Song Cheng
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Abstract

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.

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Yi-Yu Lin, Song Cheng. 2026-08-19. Holographic Bit Threads from String-Diagrammatic Quantum Information Flow. https://arxiv.org/abs/2608.19428

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