Bit thread, entanglement distillation, and entanglement of purification

Abstract

We investigate the relations between bit thread, entanglement distillation and entanglement of purification in the holographic framework. Specifically, we give a bit thread interpretation for the one-shot entanglement distillation (OSED) tensor network, which can be understood as reconstructing the geometric structure of the bulk spacetime from the entanglement information of the boundary quantum system through the "surface growth scheme". Moreover, by showing that the holographic entanglement of purification (EoP) process can be regarded as a special case of our "surface growth scheme", we naturally obtain the bit thread interpretation of the holographic EoP in our framework, which turns out to be different from the existing interpretations. Since our interpretation for holographic EoP is obtained in a more general and physical framework, the advantage of our version is that it is more natural, and possibly more reasonable to reflect the real physical entanglement structures.

arXiv comment28 pages,10 figures

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Cited by in corpus (10)

• Balanced Partial Entanglement and the Entanglement Wedge Cross Section
• Balanced Partial Entanglement and Mixed State Correlations
• The PEE aspects of entanglement islands from bit threads
• Deriving the PEE proposal from the Locking bit thread configuration
• Quantum bit threads and holographic entanglement
• Entanglement distillation toward minimal bond cut surface in tensor networks
• Note on surface growth approach for bulk reconstruction
• Non-Conformal Behavior of Holographic Entanglement Measures
• Towards bit threads in general gravitational spacetimes
• Weaving the (AdS) spaces with partial entanglement entropy threads