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Quantum information in holographic duality
Reports on Progress in Physics ( IF 18.1 ) Pub Date : 2022-03-07 , DOI: 10.1088/1361-6633/ac51b5
Bowen Chen 1 , Bartłomiej Czech 1 , Zi-Zhi Wang 1
Affiliation  

We give a pedagogical review of how concepts from quantum information theory build up the gravitational side of the anti-de Sitter/conformal field theory correspondence. The review is self-contained in that it only presupposes knowledge of quantum mechanics and general relativity; other tools—including holographic duality itself—are introduced in the text. We have aimed to give researchers interested in entering this field a working knowledge sufficient for initiating original projects. The review begins with the laws of black hole thermodynamics, which form the basis of this subject, then introduces the Ryu–Takayanagi proposal, the Jafferis–Lewkowycz–Maldacena–Suh (JLMS) relation, and subregion duality. We discuss tensor networks as a visualization tool and analyze various network architectures in detail. Next, several modern concepts and techniques are discussed: Rényi entropies and the replica trick, differential entropy and kinematic space, modular Berry phases, modular minimal entropy, entanglement wedge cross-sections, bit threads, and others. We discuss the extent to which bulk geometries are fixed by boundary entanglement entropies, and analyze the relations such as the monogamy of mutual information, which boundary entanglement entropies must obey if a state has a semiclassical bulk dual. We close with a discussion of black holes, including holographic complexity, firewalls and the black hole information paradox, islands, and replica wormholes.

中文翻译:

全息对偶中的量子信息

我们对量子信息论中的概念如何建立反德西特/共形场论对应的引力面进行了教学回顾。该评论是独立的,因为它仅假定具有量子力学和广义相对论的知识;文本中介绍了其他工具——包括全息二元性本身。我们旨在为有兴趣进入该领域的研究人员提供足以启动原创项目的工作知识。回顾从构成本主题基础的黑洞热力学定律开始,然后介绍了 Ryu-Takayanagi 提议、Jafferis-Lewkowycz-Maldacena-Suh (JLMS) 关系和次区域对偶性。我们将张量网络作为一种可视化工具进行讨论,并详细分析各种网络架构。下一个,讨论了几个现代概念和技术:Rényi 熵和复制技巧、微分熵和运动学空间、模块化 Berry 相、模块化最小熵、纠缠楔横截面、比特螺纹等。我们讨论了体几何被边界纠缠熵固定的程度,并分析了诸如互信息的一夫一妻制等关系,如果一个状态具有半经典体对偶,则边界纠缠熵必须服从。我们以对黑洞的讨论结束,包括全息复杂性、防火墙和黑洞信息悖论、岛屿和复制虫洞。我们讨论了体几何被边界纠缠熵固定的程度,并分析了诸如互信息的一夫一妻制等关系,如果一个状态具有半经典体对偶,则边界纠缠熵必须服从。我们以对黑洞的讨论结束,包括全息复杂性、防火墙和黑洞信息悖论、岛屿和复制虫洞。我们讨论了体几何被边界纠缠熵固定的程度,并分析了诸如互信息的一夫一妻制等关系,如果一个状态具有半经典体对偶,则边界纠缠熵必须服从。我们以对黑洞的讨论结束,包括全息复杂性、防火墙和黑洞信息悖论、岛屿和复制虫洞。
更新日期:2022-03-07
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