Subsystem complexity and holography
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Publication:1735635
DOI10.1007/JHEP02(2019)145zbMATH Open1411.81165arXiv1804.01561WikidataQ128384916 ScholiaQ128384916MaRDI QIDQ1735635
Author name not available (Why is that?)
Publication date: 28 March 2019
Published in: (Search for Journal in Brave)
Abstract: We study circuit complexity for spatial regions in holographic field theories. We study analogues based on the entanglement wedge of the bulk quantities appearing in the "complexity = volume" and "complexity = action" conjectures. We calculate these quantities for one exterior region of an eternal static neutral or charged black hole in general dimensions, dual to a thermal state on one boundary with or without chemical potential respectively, as well as for a shock wave geometry. We then define several analogues of circuit complexity for mixed states, and use tensor networks to gain intuition about them. We find a promising qualitative match between the holographic action and what we call the purification complexity, the minimum number of gates required to prepare an arbitrary purification of the given mixed state. On the other hand, the holographic volume does not appear to match any of our definitions of mixed-state complexity.
Full work available at URL: https://arxiv.org/abs/1804.01561
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