Bulk locality and quantum error correction in AdS/CFT

被引:499
作者
Almheiri, Ahmed [1 ]
Dong, Xi [1 ]
Harlow, Daniel [2 ]
机构
[1] Stanford Univ, Dept Phys, Stanford Inst Theoret Phys, Stanford, CA 94305 USA
[2] Princeton Univ, Princeton Ctr Theoret Sci, Princeton, NJ 08540 USA
来源
JOURNAL OF HIGH ENERGY PHYSICS | 2015年 / 04期
基金
美国国家科学基金会;
关键词
AdS-CFT Correspondence; 1/N Expansion; Black Holes in String Theory; FIELD-THEORY; ENTROPY;
D O I
10.1007/JHEP04(2015)163
中图分类号
O412 [相对论、场论]; O572.2 [粒子物理学];
学科分类号
摘要
We point out a connection between the emergence of bulk locality in AdS/CFT and the theory of quantum error correction. Bulk notions such as Bogoliubov transformations, location in the radial direction, and the holographic entropy bound all have natural CFT interpretations in the language of quantum error correction. We also show that the question of whether bulk operator reconstruction works only in the causal wedge or all the way to the extremal surface is related to the question of whether or not the quantum error correcting code realized by AdS/CFT is also a "quantum secret sharing scheme", and suggest a tensor network calculation that may settle the issue. Interestingly, the version of quantum error correction which is best suited to our analysis is the somewhat nonstandard "operator algebra quantum error correction" of Beny, Kempf, and Kribs. Our proposal gives a precise formulation of the idea of "subregion-subregion" duality in AdS/CFT, and clarifies the limits of its validity.
引用
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页数:34
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