In any physical theory, it is necessary to describe the mechanism that allows us to gather information about the physical systems that we are modelling. That is, it is necessary to describe measurements.

In classical theories, the description of measurements is frequently not explicit, often hidden under the assumption that we can neglect the effect of measurements on the state of the system of interest. However, in quantum mechanics, describing measurement processes has been problematic and a subject of discussion since its very inception. Nevertheless, from an operational point of view the problem can be bypassed in the context of non-relativistic quantum mechanics by employing Lüders rule, also known as the projection postulate. This rule prescribes how to update the state of the system after the measurement in a way consistent with the measurement outcome, through projection-valued measures (PVMs). However, as convenient as they are, projective measurements are at odds with our best understanding of quantum mechanics itself (unless we believe that measurement apparatuses are magical objects), and, furthermore, they fail to be consistent with the theory of relativity when we try to generalize their use to quantum field theory (QFT).

Indeed, idealized measurements are not suitable to describe measurements in quantum field theory, not even as an effective tool, since they are not compatible with relativistic causality, and therefore they are not consistent with the very foundational framework of QFT. Any attempt to generalize the projection postulate to quantum field theory leads to faster-than-light signalling. It should be clear from the beginning that when we talk about the causality issues of the projection postulate, we are indeed referring to superluminal causation, and not the non-locality that arises from entanglement, which can be present even between non-relativistic systems. The latter is perfectly compatible with causality as long as it does not enable signalling. In the absence of a measurement theory for QFT, how does one describe the extraction of information from quantum fields (that in particular allow us to test the theory)? How does one take into account this information for the description of future events involving the field? And last, but not least, since actual experiments are performed in laboratories involving quantum fields, how should we mathematically model these experiments?

These questions are particularly relevant for the field of relativistic quantum information (RQI), and at least the part of quantum optics where relativistic effects may play a role. Indeed, there are several landmark protocols, experimental proposals, and actual experiments in the context of quantum information (e.g., the quantum Zeno effect, the delayed choice quantum eraser experiment, or the Wigner’s friend experiment, among others) in which the ability to perform measurements and using the information of the outcomes to update the state is essential for their implementation and interpretation. To be able to formulate these scenarios in relativistic contexts, it is necessary to have a well-understood measurement framework for quantum field theory and that connects to experimentally accessible quantities.

In my talk, I will present a brief introduction to the field of relativistic quantum information and its role on this problem. Then we will discuss what are the properties that we should require of a proper measurement framework of a physical theory, and we will go over the difficulties to satisfy all of them in the context of RQI. We will also analyze what role (if any) entanglement plays in the measurement problem in QFT and in quantum optics. Finally, we will aim to formulate a consistent and satisfactory measurement theory for QFT using particle detectors as measuring tools.