Causality and strict localization

In quantum information technology, it is crucial to be able to generate single photons. Perfect single photons cannot be generated on demand; however, we can approximate them with realizable, strictly localized states. In this project, we will investigate the set of strictly localized states. This will be useful to determine how close we can approach a desired state, and will lead to valuable and novel insight from a fundamental point of view.

In quantum field theory a state is strictly localized to a region X in spacetime if the expectation value of any local observable outside X is equal to that in vacuum. Strictly localized states are important and interesting from a fundamental point of view. In addition, it is interesting to characterize these states from a practical point of view, since they correspond to states produced by on-demand sources.
 
There are many interesting questions to consider (see below). It is not realistic to answer all questions. It is possible that two students collaborate and divide tasks between them. The work will involve mathematical analysis, possibly with some analytical computer tools and/or numerics. A PhD student and the supervisor will be involved.
 
Specific tasks for the project
  • How well can a strictly localized state approximate a single-boson or single-fermion state, or any other desired state?
  • Determine the detailed properties of strictly localized states, e.g. similarly to the well-known properties of coherent states.
  • How can we explicitly generate any desired state locally (as described in the Reeh-Schlieder theorem)?
Publisert 23. juni 2020 15:06 - Sist endret 23. juni 2020 15:12

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Omfang (studiepoeng)

60