Discrete Holography: Through the Quantum Information Looking-Glass

How can we reconcile general relativity with quantum mechanics? One promising approach is the holographic principle, which posits that quantum gravity can be described by a lower-dimensional theory without gravity. This book advances the field of discrete holography by building models on discretizations of hyperbolic space, extending the AdS/CFT correspondence and enabling experimental tests of holographic predictions. The first part develops discrete bulk models on hyperbolic tilings, exploring scalar field instability and correlation functions, and proposes electric circuits as experimental platforms. The second part constructs boundary theories as disordered spin chains and analyzes their entanglement via tensor networks. The final part investigates quantum information measures—circuit complexity, geometric quantum discord, and operator algebras—to probe black hole properties in holographic dualities. This work uncovers new insights into holography and bridges theoretical concepts with experimental realizations.