Crossing versus locking: Bit threads and continuum multiflows

Abstract

Bit threads are curves in holographic spacetimes that manifest boundary entanglement, and are represented mathematically by continuum analogues of network flows or multiflows. Subject to a density bound, the maximum number of threads connecting a boundary region to its complement computes the Ryu-Takayanagi entropy. When considering several regions at the same time, for example in proving entropy inequalities, there are various inequivalent density bounds that can be imposed. We investigate for which choices of bound a given set of boundary regions can be "locked", in other words can have their entropies computed by a single thread configuration. We show that under the most stringent bound, which requires the threads to be locally parallel, non-crossing regions can in general be locked, but crossing regions cannot, where two regions are said to cross if they partially overlap and do not cover the entire boundary. We also show that, under a certain less stringent density bound, a crossing pair can be locked, and conjecture that any set of regions not containing a pairwise crossing triple can be locked, analogously to the situation for networks.

arXiv comment54 pages, 23 figures, 18 theorems

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Cited by in corpus (16)

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• Entanglement entropy from entanglement contour: higher dimensions
• The PEE aspects of entanglement islands from bit threads
• Bit thread, entanglement distillation, and entanglement of purification
• Modular conjugations in 2D conformal field theory and holographic bit threads
• Geometrizing the Partial Entanglement Entropy: from PEE Threads to Bit Threads
• Quantum bit threads and holographic entanglement
• Properties of the contraction map for holographic entanglement entropy inequalities
• Thread/State correspondence: from bit threads to qubit threads
• Bit threads on hypergraphs
• Beyond the Holographic Entropy Cone via Cycle Flows
• Towards bit threads in general gravitational spacetimes
• Weaving the (AdS) spaces with partial entanglement entropy threads
• First Law and Quantum Correction for Holographic Entanglement Contour
• Discrete Bulk Reconstruction
• Exploring the holographic entropy cone via reinforcement learning