Multipartite entanglement and topology in holography
arXiv:2006.02899 · doi:10.1007/JHEP03(2021)116
Abstract
Starting from the entanglement wedge of a multipartite mixed state we describe a purification procedure which involves the gluing of several copies. The resulting geometry has non-trivial topology and a single oriented boundary for each original boundary region. In the purified geometry the original multipartite entanglement wedge cross section is mapped to a minimal surface of a particular non-trivial homology class. In contrast each original bipartite entanglement wedge cross section is mapped to the minimal wormhole throat around each boundary. Using the bit thread formalism we show how maximal flows for the bipartite and multipartite entanglement wedge cross section can be glued together to form maximal multiflows in the purified geometry. The defining feature differentiating the flows is given by the existence of threads which cross between different copies of the original entanglement wedge. Together these demonstrate a possible connection between multipartite entanglement and the topology of holographic spacetimes.
arXiv comment28 pages, 20 figures. Minor overlap with arXiv:1906.05970 due to review of key results in section 2. v2: references added, minor changes to presentation. v3: Published version
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Cited by in corpus (7)
- Sewing spacetime with Lorentzian threads: complexity and the emergence of time in quantum gravity
- Covariant bit threads
- Towards classification of holographic multi-partite entanglement measures
- Quantum bit threads and holographic entanglement
- Entanglement Wedge Cross Section Inequalities from Replicated Geometries
- Localizing genuine multiparty entanglement in noisy stabilizer states
- Towards bit threads in general gravitational spacetimes