Detector-based measurement-induced state updates in AdS/CFT

Abstract

Conventional understandings of quantum theory hold that measurements change the state of an observed system following the L\"{u}ders update rule. Textbooks describe the application of this idea to non-relativistic systems, but extensions to relativistic and gravitating systems encounter subtleties. One consistent approach is via detector-based measurements. We study the effects of such measurements in a CFT with a holographic dual. We work out the boundary space-time regions associated to a L\"{u}ders update and how the outcome extends to modifications of the bulk gravity state. We explore information-theoretic consequences of this picture, and relate the information extracted by a measurement to updates of the semiclassical parameters of the bulk state.