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

TL;DR

This paper introduces quantum channels and their applications in quantum gravity, focusing on black holes and AdS/CFT, highlighting how quantum information concepts aid in understanding complex high-energy physics problems.

Contribution

It provides an accessible introduction to quantum channels and demonstrates their relevance to black hole information and holographic duality in high-energy physics.

Findings

Quantum channels formalize information transfer in quantum gravity.

Quantum error correction concepts apply to black hole information paradox.

Information-theoretic approaches aid in bulk reconstruction in AdS/CFT.

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.