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In this thesis, we consider the properties of measurements in quantum theoryand other operational theories. After having introduced the framework ofoperational theories, we consider a communication scheme based on anexperimental prepare-and-measure scenario and demonstrate this with differentcommunication tasks. This gives us context for how the different communicationtasks can be implemented in different theories, in doing so establishingquantum theory intuitively as an operational theory among other theories. Themain property of measurements we focus on in this work is the simulation ofmeasurements, which consists of manipulating the inputs and outputs of themeasurement devices. We study how using this process on existing measurementdevices can be used to operationally imitate new devices, and what kind ofstructure the simulation process induces on measurements. We also considerapplications of simulability. Firstly, we consider operational restrictionsimposed upon measurements. We argue that the restricted set of physicalmeasurements must be closed with respect to the simulation process since thesimulation of physical devices must lead to other physically feasible devices.We demonstrate different types of restrictions by classifying them. As a secondapplication we see how the simulation of measurements relates to compatibilityof measurements and how it can be viewed as a generalisation of it. This allowsus to present an operational principle previously known to quantum theory, theno-free-information principle, according to which any measurement that iscompatible with all other measurement must not provide any useful, andtherefore free, information about the system. Whilst this principle holds inquantum theory, there are non-classical theories for which it is violated, andso enforcing this principle may be considered a way to exclude some unphysicaltheories.

Measurement simulability and incompatibility in quantum theory and other operational theories