Physical Society Colloquium

Quantum information in space and time

Patrick Hayden

Department of Physics
Stanford University

What can quantum information theory teach us about spacetime? When it comes to black hole evaporation, quantum cloning and what lies beyond the event horizon, the theory teaches us something we should have already known: that we're confused. But the information theoretic viewpoint can also provide unexpected illumination. This talk will describe two examples of how quantum information theory can reveal unexpected and beautiful structure in spacetime.

The first example will address a basic question: where and when can a qubit be? While the no-cloning theorem of quantum mechanics prevents quantum information from being copied in space, the reversibility of microscopic physics actually requires that the information be copied in time. In spacetime as a whole, therefore, quantum information is widely replicated but in a restricted fashion. There is a simple and complete description of where and when a qubit can be located in spacetime, revealing a remarkable variety of possibilities.

The second example comes from holography. The AdS/CFT correspondence provides a concrete realization of the holographic principle, in which the physics of a “bulk” spacetime volume is completely encoded onto its boundary surface. A dictionary relates the physics of the boundary to the physics of the bulk, but the boundary interpretation of the bulk's extra dimension has always been a bit fuzzy. I'll explain one precise interpretation of that extra dimension, showing how its geometry encodes the entanglement structure of the boundary state.