Random Tensor Networks with Nontrivial Links

Explore the intricacies of random tensor networks with nontrivial links in this one-hour conference talk by Freek Witteveen. Delve into the world of quantum information theory and holographic quantum gravity as the speaker discusses the refined model of random tensor network states with arbitrary link states. Discover how entanglement properties of these networks depend on graph structure and link states, and learn about the application of tools from free probability, random matrix theory, and one-shot quantum information theory in studying these networks. Gain insights into topics such as boundary entanglement, entropy, phase transitions, replica tricks, and conditional entropy. Based on joint work with Newton Cheng, Cecilia Lancien, Geoff Penington, and Michael Walter, this talk provides a comprehensive overview of the subject matter, from basic examples to complex concepts like unique minimal cuts and permutations.

Introduction
Presentation plan
What is a tensor
Graph structure
Graph tensor
Quantum gravity
Boundary entanglement
Entropy
Entanglement
Basic example
Phase transition
Quantum information
Replica trick
Replica check
Spin model
Unique minimal cuts
Two minimal cuts
Permutations
Free Products
Conditional Entropy
Minimal Cuts