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A bstract 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 divided into N “atomic regions”, 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 O ( N 2 ) 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 O ( N 4 ) vertices whenever an embeddable bulk graph exists (thus putting the problem into the complexity class NP).
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A Dataset-Dispersion Perspective on Reconstruction Versus Recognition in Single-View 3D Reconstruction Networks
- Award ID(s):
- 2036870
- PAR ID:
- 10388254
- Date Published:
- Journal Name:
- 2021 International Conference on 3D Vision (3DV)
- Page Range / eLocation ID:
- 1331 to 1340
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/3DV53792.2021.00140
