Bulk locality and cooperative flows

Abstract

We use the 'bit thread' formulation of holographic entanglement entropy to highlight the distinction between the universally-valid strong subadditivity and the more restrictive relation called monogamy of mutual information (MMI), known to hold for geometrical states (i.e. states of holographic theories with gravitational duals describing a classical bulk geometry). In particular, we provide a novel proof of MMI, using bit threads directly. To this end, we present an explicit geometrical construction of cooperative flows which we build out of disjoint thread bundles. We conjecture that our method applies in a wide class of configurations, including ones with non-trivial topology, causal structure, and time dependence. The explicit nature of the construction reveals that MMI is more deeply rooted in bulk locality than is the case for strong subadditivity.

42 pages, 10 figures; v2: matches the published version (added figure, minor clarifying remarks, and references)

References in corpus (9)

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• Holographic entropy relations
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• Sewing spacetime with Lorentzian threads: complexity and the emergence of time in quantum gravity
• The holographic entropy arrangement
• Entanglement of Purification in Many Body Systems and Symmetry Breaking
• The connection between holographic entanglement and complexity of purification
• Bit threads and holographic entanglement of purification
• Binding Complexity and Multiparty Entanglement
• Bit threads, Einstein's equations and bulk locality
• Holographic Entropy Relations Repackaged
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• Holographic Entropy Cone with Time Dependence in Two Dimensions
• Crossing versus locking: Bit threads and continuum multiflows
• The PEE aspects of entanglement islands from bit threads
• The Quantum Entropy Cone of Hypergraphs
• Bit thread, entanglement distillation, and entanglement of purification
• Deriving the PEE proposal from the Locking bit thread configuration
• Modular conjugations in 2D conformal field theory and holographic bit threads
• Inequalities of Holographic Entanglement of Purification from Bit Threads
• Quantum bit threads and holographic entanglement
• Thread/State correspondence: from bit threads to qubit threads
• Properties of the contraction map for holographic entanglement entropy inequalities
• Holographic thermal entropy from geodesic bit threads
• Bit Threads and the Membrane Theory of Entanglement Dynamics
• Improved proof-by-contraction method and relative homologous entropy inequalities
• Towards bit threads in general gravitational spacetimes
• Holographic Shannon Entropy: The Outer Entropy of Entanglement Wedges