{"paper":{"title":"The holographic map as a conditional expectation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA","quant-ph"],"primary_cat":"hep-th","authors_text":"Thomas Faulkner","submitted_at":"2020-08-11T16:04:45Z","abstract_excerpt":"We study the holographic map in AdS/CFT, as modeled by a quantum error correcting code with exact complementary recovery. We show that the map is determined by local conditional expectations acting on the operator algebras of the boundary/physical Hilbert space. Several existing results in the literature follow easily from this perspective. The Black Hole area law, and more generally the Ryu-Takayanagi area operator, arises from a central sum of entropies on the relative commutant. These entropies are determined in a state independent way by the conditional expectation. The conditional expecta"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2008.04810","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2008.04810/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}