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

Vijay Balasubramanian, Esko Keski-Vakkuri, Nicola Pranzini

Abstract

Conventional understandings of quantum theory hold that measurements change the state of an observed system following the Lüders 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 Lüders 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.

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 Lüders 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 Lüders 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.

Paper Structure

This paper contains 12 sections, 58 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Detector-based measurements
  3. Brief review of quantum measurements
  4. Measuring a relativistic system
  5. Unruh-DeWitt measurement apparatus
  6. Measuring QFT states
  7. Measurements in AdS/CFT
  8. An alternative case.
  9. Conclusions and Outlook
  10. Slicing of the cylinder
  11. Local vs. global perspectives of measurements in CFT
  12. Localised excitations from measurements on the plane

Figures (3)

  • Figure 1: Measurement-defined regions and compatible slicings contained therein.
  • Figure 2: An example of the casual wedge $\mathcal{W}_\mathcal{D}$ in the AdS spacetime $\mathcal{M}$ and the related projection $\mathcal{D}$ on the AdS boundary $\partial\mathcal{M}$. We can reconstruct the field at any bulk point $p\in\mathcal{W}_\mathcal{D}$ such that the intersection between $\mathcal{W}_\mathcal{D}$ and the bulk past lightcone of $x_M$ is null.
  • Figure 3: Construction of a slicing respecting the spacetime regions in which a field state can be properly assigned when a measurement is performed at $x_M$.