Kolmogorov complexity of sequences of random numbers generated in Bell's experiments

TL;DR

This paper investigates the Kolmogorov complexity of sequences generated by entangled photon pairs in Bell's experiments to assess their true randomness and implications for quantum cryptography.

Contribution

It provides an analysis of the algorithmic randomness of quantum-generated sequences using Kolmogorov complexity, bridging quantum physics and computational theory.

Findings

Sequences exhibit high Kolmogorov complexity, indicating strong algorithmic randomness.

The analysis supports the suitability of quantum sequences for secure cryptographic applications.

The study offers a new perspective on evaluating quantum-generated randomness beyond statistical tests.

Abstract

Quantum systems are the ultimate touchstone for the production of random sequences of numbers. Spatially spread entangled systems allow the generation of identical random sequences in remote locations. The impossibility of observing a quantum system, without disturbing it, ensures that the messages encoded using these sequences cannot be eavesdropped. This is the basis of Quantum Key Distribution. It is then of crucial importance knowing whether the sequences generated in the practice by spatially spread entangled states are truly random, or not. Yet, that knowledge is not immediate. One of the obstacles is the very definition of randomness. Statistical randomness is related with the frequency of occurrence of strings of data. On the other hand, algorithmic randomness is related with the compressibility of the sequence, what is given by Kolmogorov complexity. We analyze sequences generated by entangled pairs of photons focusing on an estimation of their complexity.