Martin L\"{o}f - Solovay - Chaitin Axiom of Reduction versus Von Mises - Church Axiom of Reduction

TL;DR

The paper presents experimental evidence suggesting that quantum coin tosses do not pass certain randomness tests, challenging the Martin Löf - Solovay - Chaitin Axiom of Reduction and proposing a weaker alternative based on game theory.

Contribution

It provides experimental data indicating the need to replace the Martin Löf - Solovay - Chaitin Axiom with the Von Mises - Church Axiom of Reduction in quantum mechanics.

Findings

Quantum coin tosses fail the Iterated Logarithm Randomness' Test.

Experimental violation of the Martin Löf - Solovay - Chaitin Axiom observed.

Proposes the Von Mises - Church Axiom as a weaker alternative.

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 L\"{o}f - 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.