Measuring quantum fields with particle detectors and machine learning
The model for measurements used in quantum mechanics (based on the projection postulate) cannot be extended to model measurements of quantum fields, since they are incompatible with relativity. We will see that measurements performed with particle detectors (i.e., localized non-relativistic quantum systems that couple covariantly to quantum fields) are consistent with relativity, and that they allow us to build a consistent measurement theory for QFT. For this measurement framework to be of practical use, we need to understand how we can measure specific properties of the field using a particle detector. I will show that there is a simple fixed measurement protocol that allows us to extract essentially all the information about the field that the detector gathers, and that this information can then be interpreted to study a specific targeted feature using machine learning techniques. Specifically, I will examine two examples in which we use a neural network to extract global information about the field (boundary conditions and temperature) performing local measurements, taking advantage of the fact that this global information is stored locally by the field, albeit in a scrambled way.
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