Pure Quantum States Are Fundamental, Mixtures (Composite States) Are Mathematical Constructions: An Argument Using Algorithmic Information Theory

From the philosophical viewpoint, two interpretations of the quantum measurement process are possible: According to the first interpretation, when we measure an observable, the measured system moves into one of the eigenstates of this observable (“the wave function collapses”); in other words, the Universe “branches” by itself, due to the very measurement procedure, even if we do not use the result of the measurement. According to the second interpretation, the system simply moves into a mixture of eigenstates, and the actual “branching” occurs only when an observer reads the measurement results. According to the first interpretation, a mixture is a purely mathematical construction, and in the real physical world, a mixture actually means that the system is in one of the “component” states. In this paper, we analyze this difference from the viewpoint of the algorithmic information theory; as a result of this analysis, we argue that only pure quantum states are fundamental, while mixtures are simply useful mathematical constructions.