Quantumness, Randomness and Computability

TL;DR

This paper explores the deep connections between quantum phenomena, randomness, and computability, highlighting how quantum mechanics challenges classical notions of randomness and introduces concepts like incomputability.

Contribution

It provides a comprehensive review of the relationship between Bell inequality violations, non-signaling, and randomness, and discusses the role of algorithmic information theory in defining quantum randomness.

Findings

Bell inequality violations imply intrinsic quantum randomness

Algorithmic information theory offers a necessary condition for quantum randomness

Incomputability has significant implications for understanding quantum physics

Abstract

Randomness plays a central rol in the quantum mechanical description of our interactions. We review the relationship between the violation of Bell inequalities, non signaling and randomness. We discuss the challenge in defining a random string, and show that algorithmic information theory provides a necessary condition for randomness using Borel normality. We close with a view on incomputablity and its implications in physics.