An Introduction to Algorithmic Information Theory and Quantum Mechanics
Samuel Epstein · HAL (Le Centre pour la Communication Scientifique Directe) · 2023
This article presents a survey of published and unpublished material of the intersection of Algorithmic Information Theory and Quantum Mechanics. It is, to the author's knowledge, the first of its type. Three different notions of the algorithmic content of quantum states are reviewed. Notions of algorithmic quantum typicality and mutual information are introduced. The relationship between algorithmic information and quantum measurements is explored. One of the surprising results is that an overwhelming majority of quantum (pure and mixed) states, when undertaking decoherence, will result in a classical probability with no algorithmic information. Thus most quantum states decohere into white noise. A quantum analouge of Martin Löf random sequence is reviewed. Algorithmic Information Theory presents new complications for the Many Worlds Theory, as it conflicts with the Independence Postulate. When algorithmically complicated processes are ruled out, measurements are required to produce distributions over quantum states that have cloneable information.