In contrast with software-generated randomness (called pseudo-randomness), quantum randomness can be proven incomputable; that is, it is not exactly reproducible by any algorithm. We provide experimental evidence of incomputability\char22{}an asymptotic property\char22{}of quantum randomness by performing finite tests of randomness inspired by algorithmic information theory.

The increasing numbers of textual documents from diverse sources such as different websites (e.g. social networks, news, magazines, blogs and medical recommendation websites), publications and articles and medical prescriptions leads to massive amounts of daily complex data. This phenomenon has caused many researchers to focus on analysing the content and measuring the similarities among the documents and texts to cluster them. One popular method to measure the similarity between documents is to represent the documents as vectors and measure the similarity among them based on the angle or Euclidean distance between each pair. By only considering these two criteria for similarity measurement, we may miss important underlying similarities in this area. We propose a new method, TS-SS, to measure the similarity level among documents, in such a way that one hopes to better understand which documents are more (or less) similar. This similarity level can be used as a handy measure for clustering and recommendation systems for documents. It also can be used to show top n similar documents to a particular document or a search query. Our study gives insights on the drawbacks of geometrical and non-geometrical similarity measures and provides a novel method to combine the other geometric criteria into a method to measure the similarity level among documents from new prospective. We apply Euclidean distance, Cosine similarity and our new method on four labelled datasets. Finally we report how these three geometrical similarity measures perform in terms of similarity level and clustering purity using four evaluation techniques. The evaluations' results show that our new model outperforms the other measures.

The advantages of quantum random number generators (QRNGs) over pseudo-random number generators (PRNGs) are normally attributed to the nature of quantum measurements. This is often seen as implying the superiority of the sequences of bits themselves generated by QRNGs, despite the absence of empirical tests supporting this. Nonetheless, one may expect sequences of bits generated by QRNGs to have properties that pseudo-random sequences do not; indeed, pseudo-random sequences are necessarily computable, a highly nontypical property of sequences. In this paper, we discuss the differences between QRNGs and PRNGs and the challenges involved in certifying the quality of QRNGs theoretically and testing their output experimentally. While QRNGs are often tested with standard suites of statistical tests, such tests are designed for PRNGs and only verify statistical properties of a QRNG, but are insensitive to many supposed advantages of QRNGs. We discuss the ability to test the incomputability and algorithmic complexity of QRNGs. While such properties cannot be directly verified with certainty, we show how one can construct indirect tests that may provide evidence for the incomputability of QRNGs. We use these tests to compare various PRNGs to a QRNG, based on superconducting transmon qutrits and certified by the Kochen–Specker theorem, to see whether such evidence can be found in practice. While our tests fail to observe a strong advantage of the quantum random sequences due to algorithmic properties, the results are nonetheless informative: some of the test results are ambiguous and require further study, while others highlight difficulties that can guide the development of future tests of algorithmic randomness and incomputability.