Quantum Information Approaches to Quantum Gravity

Abstract

In this thesis we apply techniques from quantum information theory to study quantum gravity within the framework of the anti-de Sitter / conformal field theory correspondence (AdS/CFT). Through AdS/CFT, progress has been made in understanding the structure of entanglement in quantum field theories, and in how gravitational physics can emerge from these structures. However, this understanding is far from complete and will require the development of new tools to quantify correlations in CFT. This thesis presents refinements of a duality between operator product expansion (OPE) blocks in the CFT, giving the contribution of a conformal family to the OPE, and geodesic integrated fields in AdS which are diffeomorphism invariant quantities. This duality was originally discovered in the maximally symmetric setting of pure AdS dual to the CFT ground state. In less symmetric states the duality must be modified. Working with excited states within AdS${}_3$/CFT${}_2$, this thesis shows how the OPE block decomposes into more fine-grained CFT observables that are dual to AdS fields integrated over non-minimal geodesics. Additionally, this thesis contains results on the dynamics of entanglement measures for general quantum systems. Results are presented for the family of quantum Rényi entropies and entanglement negativity. Rényi entropies are studied for general dynamics by imposing special initial conditions. Around pure, separable initial states, all Rényi entropies grow with the same timescale at leading, and next-to-leading order. Mathematical tools are developed for the differentiation of non-analytic matrix functions with respect to constrained arguments and are used to construct analytic expressions for derivatives of negativity. We establish bounds on the rate of change of state distinguishability and the rate of entanglement growth for closed systems. Note: Abstract shortened.

PhD Thesis, contains previously published papers and additional work, 135 pages

References in corpus (34)

• Experimental quantum teleportation
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Nonlinear atom interferometer surpasses classical precision limit
• Complexity and Shock Wave Geometries
• Lieb-Robinson bounds and the generation of correlations and topological quantum order
• Quantum Computation as Geometry
• Climbing the Jaynes-Cummings Ladder and Observing its Sqrt(n) Nonlinearity in a Cavity QED System
• Holographic representation of local bulk operators
• Causality & holographic entanglement entropy
• Measuring entanglement growth in quench dynamics of bosons in an optical lattice
• Sudden Birth Versus Sudden Death of Entanglement in Multipartite Systems
• A holographic proof of the strong subadditivity of entanglement entropy
• Gravity solutions for the D1-D5 system with angular momentum
• General entanglement scaling laws from time evolution
• Entwinement and the emergence of spacetime
• Observables, gravitational dressing, and obstructions to locality and subsystems
• Operator Dictionaries and Wave Functions in AdS/CFT and dS/CFT
• Relative Entropies in Conformal Field Theory
• Holographic Holes in Higher Dimensions
• D1-D5-P microstates at the cap
• Thermal state entanglement in harmonic lattices
• Experimental bound entanglement in a four-photon state
• Nuts and Bolts for Creating Space
• Entanglement entropy scaling in the bilayer Heisenberg spin system
• Casting Shadows on Holographic Reconstruction
• Entwinement in discretely gauged theories
• Entanglement of Purification in Many Body Systems and Symmetry Breaking
• Entanglement entropy in three dimensional gravity
• From Conformal Blocks to Path Integrals in the Vaidya Geometry
• Kinematic space for conical defects
• Bulk fields from the boundary OPE
• Universal Bounds on the Time Evolution of Entanglement Entropy
• A geodesic Witten diagram description of holographic entanglement entropy and its quantum corrections
• A characteristic function approach to the Jaynes-Cummings model revivals