Bit Threads and Holographic Monogamy

Abstract

Bit threads provide an alternative description of holographic entanglement, replacing the Ryu-Takayanagi minimal surface with bulk curves connecting pairs of boundary points. We use bit threads to prove the monogamy of mutual information (MMI) property of holographic entanglement entropies. This is accomplished using the concept of a so-called multicommodity flow, adapted from the network setting, and tools from the theory of convex optimization. Based on the bit thread picture, we conjecture a general ansatz for a holographic state, involving only bipartite and perfect-tensor type entanglement, for any decomposition of the boundary into four regions. We also give new proofs of analogous theorems on networks.

arXiv comment58 pages, 5 figures; v2: improvements to presentation; references added; essentially matches published version

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Cited by in corpus (50)

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• Lorentzian threads as 'gatelines' and holographic complexity
• Reflected entropy, symmetries and free fermions
• Bit threads and holographic entanglement of purification
• Bit threads, Einstein's equations and bulk locality
• Quantum Extremal Surfaces and the Holographic Entropy Cone
• Entanglement entropy from entanglement contour: higher dimensions
• Crossing versus locking: Bit threads and continuum multiflows
• Holographic scattering requires a connected entanglement wedge
• Majorana dimers and holographic quantum error-correcting codes
• The PEE aspects of entanglement islands from bit threads
• Negativity Spectra in Random Tensor Networks and Holography
• Superbalance of Holographic Entropy Inequalities
• The Quantum Entropy Cone of Hypergraphs
• Hyperbolic Fracton Model, Subsystem Symmetry, and Holography II: The Dual Eight-Vertex Model
• A holographic inequality for $N=7$ regions
• Bit thread, entanglement distillation, and entanglement of purification
• Holographic Entropy Inequalities and Multipartite Entanglement
• Deriving the PEE proposal from the Locking bit thread configuration
• Holographic Cone of Average Entropies
• Tripartite information at long distances
• Mixed-state entanglement and information recovery in thermalized states and evaporating black holes
• Inequalities of Holographic Entanglement of Purification from Bit Threads
• Quantum bit threads and holographic entanglement
• Perfect tensor hyperthreads
• Testing holographic entropy inequalities in 2+1 dimensions
• Towards a complete classification of holographic entropy inequalities
• Properties of the contraction map for holographic entanglement entropy inequalities
• Holographic thermal entropy from geodesic bit threads
• Entanglement Wedge Cross Section with Gauss-Bonnet Corrections and Thermal Quench
• Multipartite entanglement and topology in holography
• A gap between holographic and quantum mechanical extreme rays of the subadditivity cone
• Bit Threads and the Membrane Theory of Entanglement Dynamics
• A framework for generalizing toric inequalities for holographic entanglement entropy
• Improved proof-by-contraction method and relative homologous entropy inequalities
• Multipartite Optimized Correlation Measures and Holography
• Beyond the Holographic Entropy Cone via Cycle Flows
• Purely GHZ-like entanglement is forbidden in holography
• Towards bit threads in general gravitational spacetimes
• The Markov gap for geometric reflected entropy
• First Law and Quantum Correction for Holographic Entanglement Contour
• Does connected wedge imply distillable entanglement?
• Bit Threads: From Entanglement to Geometric Entropies
• Illuminating entanglement shadows of BTZ black holes by a generalized entanglement measure
• Entangled universes
• Exploring the holographic entropy cone via reinforcement learning
• Hyperthreads in holographic spacetimes