2018/04/30 by Ricardo Espíndola, Alberto Güijosa, Alberto Guijosa +1 · 3 citations
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Black Holes and Theoretical Physics #Boundary (topology) #Duality (order theory) #Generalization #Geometry and complex manifolds #Holography #Quantum entanglement #Wedge (geometry) #gr-qc #hep-th
paper · pdf · doi:10.1140/epjc/s10052-018-6140-2
published as Eur.Phys.J. C78 (2018) no.8, 646 · 30 pages, 5 figures. v2: references added, typos corrected. v3: published version
openalex created_date 2018/04/24 · openalex publication_date 2018/08/01 · arxiv created 2018/08/19 · arxiv updated 2018/08/21 · openalex updated_date 2026/08/05
In the holographic correspondence, subregion duality posits that knowledge of the mixed state of a finite spacelike region of the boundary theory allows full reconstruction of a specific region of the bulk, known as the entanglement wedge. This statement has been proven for local bulk operators. In this paper, specializing first for simplicity to a Rindler wedge of \hbox AdS3 , we find that generic curves within the wedge are in fact not fully reconstructible with entanglement entropies in the corresponding boundary region, even after using the most general variant of hole-ography, which was recently shown to suffice for reconstruction of arbitrary spacelike curves in the Poincaré patch. This limitation is an analog of the familiar phenomenon of entanglement shadows, which we call ‘entanglement shade’. We overcome it by showing that the information about the nonreconstructible curve segments is encoded in a slight generalization of the concept of entanglement of purification, whose holographic dual has been discussed very recently. We introduce the notion of ‘differential purification’, and demonstrate that, in combination with differential entropy, it enables the complete reconstruction of all spacelike curves within an arbitrary entanglement wedge in any 3-dimensional bulk geometry.