Kolmogorov complexity of Bell's experiment time series

M. AGUERO; M. KOVALSKY; A. HNILO

Cancún

Conferencia; X Iberoamerican Optics Meeting. XIII Latin American Meeting on Optics, Laser and Aplications. Mexican Optics and photonics Meeting. RIAO- OPTILAS-MOPM 2019 Conference; 2019

Measurements performed on quantum states are believed to be the ultimate source of sequences of random numbers. Spatially spread entangled states allow the generation of correlated random sequences in remote locations. The impossibility of observing a quantum state, without disturbing it, ensures that the messages encoded using these sequences cannot be eavesdropped. This is the basis of Quantum Key Distribution, an application of quantum principles of main interest. 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. ?Algorithmic? randomness is related with compressibility of the sequence, what is given by algorithmic (or Kolmogorov) complexity. In this contribution, sequences generated by entangled pairs of photons in a famous Bell?s experiment are analyzed, focusing on estimations of their Kolmogorov complexity. Standard tests of statistical randomness are also applied. The main conclusion of this study is that, although satisfactorily random sequences are generated in many cases, it is not safe taking randomness for granted in experimentally generated sequences, even if they violate the involved Bell?s inequality by a wide margin with a maximally entangled state . This result may also imply a fundamental change in the way Quantum Mechanics is understood.