Martin Löf - Solovay - Chaitin Axiom of Reduction versus Von Mises - Church Axiom of Reduction

Abstract

Under the assumption that the quantum random number generator Quantis by Id Quantique is a fair quantum coin, experimental indications of the fact that independent tosses of a quantum coin don't pass the Iterated Logarithm Randomness' Test are shown. The consequential observed experimental violation of the Martin Löf - Solovay - Chaitin Axiom of Reduction of Quantum Mechanics is then interpreted as the indication of the necessity of replacing it with the weaker Von Mises - Church Axiom of Reduction whose Game Theoretic meaning is explained.