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

KOVALSKY, MARCELO G.; HNILO, ALEJANDRO A.; AGÜERO, MÓNICA B.

Physical Review A

American Physical Society

Año: 2018 vol. 98

2469-9926

Quantum states are the ultimate criterion to produce sequences of random numbers. Spatially spread entangledstates allow the generation of correlated random sequences in remote locations. The impossibility of observinga quantum state, without disturbing it, ensures that the messages encoded using these sequences cannot beeavesdropped upon. This is the basis of quantum key distribution. It is then of crucial importance knowingwhether 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. Algorithmic randomness is relatedwith compressibility of the sequence, which is given by Kolmogorov complexity. Sequences generated byentangled pairs of photons are analyzed, focusing on estimations of their complexity. Standard tests of statisticalrandomness are also applied.