# The algorithmic randomness of quantum measurements

## TL;DR

This paper discusses the distinction between computable probability sources and the algorithmic randomness of quantum measurement outcomes, emphasizing the philosophical and computational nuances of defining randomness.

## Contribution

It clarifies the difference between computability of probability sources and the algorithmic randomness of generated sequences, and discusses philosophical implications.

## Key findings

- No known algorithm defines the abstract meaning of randomness.
- Quantum measurement outcomes can be incompressible but not necessarily generated by a computable source.
- The paper emphasizes the philosophical debate on the nature of randomness.

## Abstract

This paper is a comment on the paper "Quantum Mechanics and Algorithmic Randomness" was written by Ulvi Yurtsever \cite{Yurtsever} and the briefly explanation of the algorithmic randomness of quantum measurements results. There are differences between the computability of probability sources, ( which means there is an algorithm that can define the way that random process or probability source generates the numbers ) and the algorithmic randomness of the sequences or strings which are produced by a source. We may have the source without a computable algorithm for that but it can produce compressible or incompressible strings. For example, so far there is no computable algorithm that can define the abstract meaning of randomness even the easiest one, Bernoulli probability distribution. Historically and philosophically there many scientist believe the existence of the algorithm for a random process is a contradiction because in their opinion, in the definition of a random variable, implicitly assumed that there is no reason for the happening of an event and we just know the probabilities. There is however no need to enter into this matter here. As in the paper mentioned, all the algorithms for simulating a random process try to pass the statistical tests and be close to the abstract meaning of it.