Searching for evidence of algorithmic randomness and incomputability in the output of quantum random number generators

Ideal quantum random number generators (QRNGs) can produce algorithmically and thus incomputable sequences, in contrast to pseudo-random generators. However, the verification of presence algorithmic randomness incomputability is a nontrivial task. We present results search for output from two different QRNGs, performed by applying tests based on Solovay-Strassen test primality Chaitin-Schwartz theorem. The first QRNG uses measurements vacuum fluctuations. second polarization entangled single photons; this generator, we use looped (and highly compressible) strings that also allow us assess ability detect repeated bit patterns. Compared previous randomness, our study increases statistical power almost 3 orders magnitude.