Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2102.02066

Modave Lectures on Quantum Information: An Introduction to Channels and Applications to Black Holes and AdS/CFT

Aidan Chatwin-Davies

Published Feb 12, 2021• 1 citation
arXivHTMLPDF

Abstract

These notes introduce a handful of core ideas from quantum information science that figure prominently in modern research on quantum gravity. The central concept that forms the base of these notes is that of a quantum channel; that is, the most general physically-reasonable map between quantum states and between operators on Hilbert space. After reviewing some fundamentals, we will study channels and their properties, and then go on to formulate quantum error correction in terms of quantum channels. Along the way, we will see how a handful of problems in high energy physics, such as the black hole information problem and bulk reconstruction in AdS/CFT, can be cast in the information-theoretic language being set up.

DOI
10.22323/1.389.0003

Related papers

6.S899 Project Report Tensor Networks, Quantum Error Correction, and AdS/CFT

John C. Napp

In recent years, the high energy physics community has become increasingly interested in entanglement, especially since it seems that, in some sense, spacetime itself may arise from entanglement [1]. Since dealing with entanglement is a strong point of quantum information theory, it’s perhaps not surprising that quantum information is working its way into some work in this area, including work in the context of the AdS/CFT correspondence, a duality between quantum theories of gravity in d + 1 dimensions and conformal field theories in d dimensions. In this report, I survey at a very schematic level some recent work which lies in the intersection of quantum information theory (broadly speaking) and the AdS/CFT correspondence, especially in relation to tensor network models of holography. For completion, I won’t assume background which wasn’t covered in class, and so I briefly review relevant features of AdS/CFT and tensor networks.

•Jan 1, 2015•0 citations

Holographic tensor network models and quantum error correction: a topical review

A. Jahn, Jens Eisert

Abstract Recent progress in studies of holographic dualities, originally motivated by insights from string theory, has led to a confluence with concepts and techniques from quantum information theory. A particularly successful approach has involved capturing holographic properties by means of tensor networks which not only give rise to physically meaningful correlations of holographic boundary states, but also reproduce and refine features of quantum error correction in holography. This topical review provides an overview over recent successful realizations of such models. It does so by building on an introduction of the theoretical foundations of AdS/CFT and necessary quantum information concepts, many of which have themselves developed into independent, rapidly evolving research fields.

arXiv:2102.02619•Quantum Science and Technology•May 18, 2021•102 citations

An Introduction to the Formalism of Quantum Information

Carlos Navarrete–Benlloch

Quantum information is an emerging field which has attracted a lot of attention in the last fifteen years or so. It is a broad subject which covers from the most applied questions (e.g., how to build quantum computers or secure cryptographic systems), to the most theoretical problems concerning the formalism of quantum mechanics, its complexity, and its potential to go beyond classical physics. I have written these notes as an introduction to the formalism of quantum information, trying to show how it is a natural progression from an undergraduate course on quantum mechanics (just as I felt it was for me). Hence, these are mainly notes about the language of quantum information and the meaning of its terms, not about its applications. They do not intend to be an exhaustive review about the field, but just a logical sequence of ideas, concepts and definitions, building up towards the continuous variables formalism, which actually takes over most of the notes. In this way, most of the results are stated without proof, and I haven't been careful with references; this is a work in progress, and I intend to add such things in the future. In any case, most of the topics that I introduce have been thoroughly covered in previous books and reviews, and with this notes I only intend to give my point of view, as well as to introduce the different topics and objects in exactly the way I work with and think about them, hoping it will be useful, especially for the people who are starting in the field. These notes originated in 2010 as a way of studying for my close collaboration with Raúl García-Patrón and Nicolas J. Cerf, to whom I am deeply grateful for guidance and incredibly clarifying discussions. They benefited greatly as well from the weeks I spent in Doha with Hyunchul Nha and his group in 2012, especially from discussions with him and Ho-Joon Kim.

arXiv:1504.05270•Apr 21, 2015•2 citations

Quantum gravity and quantum information

Raphael Bousso A

Quantum information, quantum black holes, and new results in QFT. 0:00:00 Slide 1 0:06:38 Slide 2 0:13:16 Slide 3 0:19:54 Slide 4 0:26:32 Slide 5 0:33:10 Slide 6 0:39:47 Slide 7 0:46:25 Slide 8 0:53:03 Slide 9 0:59:41 Slide 10 1:06:19 Slide 11

•Jan 1, 2019•0 citations

Desigualdades geométricas para correção de erros aproximada e algumas palavras sobre holografia

Guilherme Camargo Fiusa

In this work, we investigate some applications of quantum information theory motivated by high-energy physics. There is strong evidence suggesting that entanglement is deeply connected with the geometry of spacetime, which leads to surprising applications of quantum information theory in the AdS/CFT correspondence and holography. We start by reviewing the fundamental concepts of the AdS/CFT correspondence which play a key role in bulk-boundary reconstruction, in particular, we explore some features which suggest that one must interpret the encoding of information in the correspondence as a quantum errorcorrecting code. We discuss the fundamentals of error correction, exploring the formalisms of operator algebra and stabilizer codes. Then, we establish the concrete connection between the two main concepts by showing examples of quantum error-correcting codes that serve as a toy model for AdS/CFT. We illustrate how the 3-qutrit code and the HaPPY code can be powerful tools to explore the correspondence analytically and to solve apparent paradoxes. Following recent results, using quantum error correction, that suggest an intrinsic incompatibility of quantum gravity with global symmetries, we explore approximate error-correcting codes and asymmetric codes as a way to better understand the consequences in a quantum resource-theoretic way. Finally, we discuss our original contribution: geometric bounds for approximate quantum error correction. We calculate our bounds for three typical quantum channels that model the lack of exactness in error correction, namely, dephasing, depolarizing, and amplitude damping channels. The implications of our bounds for AdS/CFT are somewhat elusive; nonetheless, we provide a new approach to benchmark approximations in error correction performance, which may be of high interest for AdS/CFT and its corresponding absence of global symmetries.

•Sep 6, 2022•0 citations

Quantum Information Theory -- Lecture Notes

Christoph Dittel

These lecture notes provide an introduction to quantum information and quantum computation, which are strongly related disciplines and subject of intense research. The lecture notes contain only a small selection of topics in these disciplines, with the aim of providing you with an overview and a basic introduction. The corresponding lecture series is available on my YouTube channel.

arXiv:2311.12442•Nov 21, 2023•0 citations
These notes introduce a handful of core ideas from quantum information science that figure prominently in modern research on quantum gravity. The central concept that forms the base of these notes is that of a quantum channel; that is, the most general physically-reasonable map between quantum states and between operators on Hilbert space. After reviewing some fundamentals, we will study channels and their properties, and then go on to formulate quantum error correction in terms of quantum channels. Along the way, we will see how a handful of problems in high energy physics, such as the black hole information problem and bulk reconstruction in AdS/CFT, can be cast in the information-theoretic language being set up.
In recent years, the high energy physics community has become increasingly interested in entanglement, especially since it seems that, in some sense, spacetime itself may arise from entanglement [1]. Since dealing with entanglement is a strong point of quantum information theory, it’s perhaps not surprising that quantum information is working its way into some work in this area, including work in the context of the AdS/CFT correspondence, a duality between quantum theories of gravity in d + 1 dimensions and conformal field theories in d dimensions. In this report, I survey at a very schematic level some recent work which lies in the intersection of quantum information theory (broadly speaking) and the AdS/CFT correspondence, especially in relation to tensor network models of holography. For completion, I won’t assume background which wasn’t covered in class, and so I briefly review relevant features of AdS/CFT and tensor networks.
Abstract Recent progress in studies of holographic dualities, originally motivated by insights from string theory, has led to a confluence with concepts and techniques from quantum information theory. A particularly successful approach has involved capturing holographic properties by means of tensor networks which not only give rise to physically meaningful correlations of holographic boundary states, but also reproduce and refine features of quantum error correction in holography. This topical review provides an overview over recent successful realizations of such models. It does so by building on an introduction of the theoretical foundations of AdS/CFT and necessary quantum information concepts, many of which have themselves developed into independent, rapidly evolving research fields.
Quantum information is an emerging field which has attracted a lot of attention in the last fifteen years or so. It is a broad subject which covers from the most applied questions (e.g., how to build quantum computers or secure cryptographic systems), to the most theoretical problems concerning the formalism of quantum mechanics, its complexity, and its potential to go beyond classical physics. I have written these notes as an introduction to the formalism of quantum information, trying to show how it is a natural progression from an undergraduate course on quantum mechanics (just as I felt it was for me). Hence, these are mainly notes about the language of quantum information and the meaning of its terms, not about its applications. They do not intend to be an exhaustive review about the field, but just a logical sequence of ideas, concepts and definitions, building up towards the continuous variables formalism, which actually takes over most of the notes. In this way, most of the results are stated without proof, and I haven't been careful with references; this is a work in progress, and I intend to add such things in the future. In any case, most of the topics that I introduce have been thoroughly covered in previous books and reviews, and with this notes I only intend to give my point of view, as well as to introduce the different topics and objects in exactly the way I work with and think about them, hoping it will be useful, especially for the people who are starting in the field. These notes originated in 2010 as a way of studying for my close collaboration with Raúl García-Patrón and Nicolas J. Cerf, to whom I am deeply grateful for guidance and incredibly clarifying discussions. They benefited greatly as well from the weeks I spent in Doha with Hyunchul Nha and his group in 2012, especially from discussions with him and Ho-Joon Kim.
In this work, we investigate some applications of quantum information theory motivated by high-energy physics. There is strong evidence suggesting that entanglement is deeply connected with the geometry of spacetime, which leads to surprising applications of quantum information theory in the AdS/CFT correspondence and holography. We start by reviewing the fundamental concepts of the AdS/CFT correspondence which play a key role in bulk-boundary reconstruction, in particular, we explore some features which suggest that one must interpret the encoding of information in the correspondence as a quantum errorcorrecting code. We discuss the fundamentals of error correction, exploring the formalisms of operator algebra and stabilizer codes. Then, we establish the concrete connection between the two main concepts by showing examples of quantum error-correcting codes that serve as a toy model for AdS/CFT. We illustrate how the 3-qutrit code and the HaPPY code can be powerful tools to explore the correspondence analytically and to solve apparent paradoxes. Following recent results, using quantum error correction, that suggest an intrinsic incompatibility of quantum gravity with global symmetries, we explore approximate error-correcting codes and asymmetric codes as a way to better understand the consequences in a quantum resource-theoretic way. Finally, we discuss our original contribution: geometric bounds for approximate quantum error correction. We calculate our bounds for three typical quantum channels that model the lack of exactness in error correction, namely, dephasing, depolarizing, and amplitude damping channels. The implications of our bounds for AdS/CFT are somewhat elusive; nonetheless, we provide a new approach to benchmark approximations in error correction performance, which may be of high interest for AdS/CFT and its corresponding absence of global symmetries.