Discrete Bulk Reconstruction
arXiv:2210.15601 · doi:10.1007/JHEP04(2023)037
Abstract
According to the AdS/CFT correspondence, the geometries of certain spacetimes are fully determined by quantum states that live on their boundaries -- indeed, by the von Neumann entropies of portions of those boundary states. This work investigates to what extent the geometries can be reconstructed from the entropies in polynomial time. Bouland, Fefferman, and Vazirani (2019) argued that the AdS/CFT map can be exponentially complex if one wants to reconstruct regions such as the interiors of black holes. Our main result provides a sort of converse: we show that, in the special case of a single 1D boundary, if the input data consists of a list of entropies of contiguous boundary regions, and if the entropies satisfy a single inequality called Strong Subadditivity, then we can construct a graph model for the bulk in linear time. Moreover, the bulk graph is planar, it has vertices (the information-theoretic minimum), and it's ``universal,'' with only the edge weights depending on the specific entropies in question. From a combinatorial perspective, our problem boils down to an ``inverse'' of the famous min-cut problem: rather than being given a graph and asked to find a min-cut, here we're given the values of min-cuts separating various sets of vertices, and need to find a weighted undirected graph consistent with those values. Our solution to this problem relies on the notion of a ``bulkless'' graph, which might be of independent interest for AdS/CFT. We also make initial progress on the case of multiple 1D boundaries -- where the boundaries could be connected via wormholes -- including an upper bound of vertices whenever a planar bulk graph exists (thus putting the problem into the complexity class ).
arXiv comment41 pages, 18 figures. Comments welcomed! v2: new corollaries 2.3 and 4.5 with more explicit discussions of computability, additional references and discussion
References in corpus (26)
- Holographic Derivation of Entanglement Entropy from AdS/CFT
- A Covariant Holographic Entanglement Entropy Proposal
- Cool horizons for entangled black holes
- Holographic quantum error-correcting codes: Toy models for the bulk/boundary correspondence
- Bulk Locality and Quantum Error Correction in AdS/CFT
- Holographic duality from random tensor networks
- Maximin Surfaces, and the Strong Subadditivity of the Covariant Holographic Entanglement Entropy
- The Ryu-Takayanagi Formula from Quantum Error Correction
- Holographic Mutual Information is Monogamous
- The Holographic Entropy Cone
- Towards a full solution of the large N double-scaled SYK model
- Extremal Surface Barriers
- Towards Bulk Metric Reconstruction from Extremal Area Variations
- Finding Pythons in Unexpected Places
- Holographic Entropy Relations Repackaged
- Crossing versus locking: Bit threads and continuum multiflows
- Holographic Entropy Cone with Time Dependence in Two Dimensions
- Quantum Max-flow/Min-cut
- Maximin is Not Enough
- The Symmetrized Holographic Entropy Cone
- Multipartite Quantum States and their Marginals
- Tensor networks for dynamic spacetimes
- Hypergraph min-cuts from quantum entropies
- More of the Bulk from Extremal Area Variations
- An Entropic Lens on Stabilizer States
- The Complexity of Identifying Ryu-Takayanagi Surfaces in AdS3/CFT2