Quantum theory is the foundation for our current understanding of most natural phenomena. The core principles of quantum theory, namely Born's rule and the state-update rule, revolve around measurement. The distinction between measured and not measured is unavoidably fuzzy in principle (even if it is clear enough in practice), but using quantum theory requires drawing that line somewhere. That situation is called the measurement problem. This article introduces the core principles of quantum theory with emphasis on their relationship to the physical process of measurement.
To help clarify the content of the core principles, an observable is represented by a set of projection operators representing the possible outcomes when the observable is measured, and states (which are used to tell quantum theory what we know so far about the system's history) are represented by positive linear functionals on the algebra of observables.
