Essay: Emergent Holographic Spacetime from Quantum Information
Tadashi Takayanagi
Abstract
Holographic duality describes gravitational theories in terms of quantum many-body systems. In holography, quantum information theory provides a crucial tool that directly connects microscopic structures of these systems to the geometries of gravitational spacetimes. One manifestation is that the entanglement entropy in quantum many-body systems can be calculated from the area of an extremal surface in the corresponding gravitational spacetime. This implies that a gravitational spacetime can emerge from an enormous number of entangled qubits. In this Essay, I will discuss open problems in this area of research, considering recent developments and outlining future prospects towards a complete understanding of quantum gravity. The first step in this direction is to understand what kind of quantum circuits each holographic spacetime corresponds to, drawing on recent developments in quantum complexity theories and studying concrete examples of holography in string theory. Next, we should extend the concept of holography to general spacetimes, e.g., those spacetimes which appear in realistic cosmologies, by utilizing the connections between quantum information and holography. To address the fundamental question of how time emerges, I will propose the concepts of pseudoentropy and timelike entanglement as a useful tool in our exploration. Part of a series of Essays in Physical Review Letters which concisely present author visions for the future of their field.