Unpredictability and Randomness

Masanobu Inubushi, Kazuyuki Yoshimura, Kenichi Arai +1 more

Physical random bit generators (RBGs) that generate unpredictable bits at high speed are now of increasing importance in information science and technology. since they are expected to generate unpredictable random bits with high speed. From the viewpoint of applications for security, it is a crucial issue to be able to give a guarantee of the unpredictability of random bits. In this paper, we review research on physical RBGs, particularly focusing our attention on the studies of the unpredictability of random bits generated by laser systems, which are promising entropy sources for physical RBGs. Finally, we report recent research results on noise-robustness, which could be crucial for reliability of physical RBG.

Vincenzo Manca, Vincenzo Bonnici

Clas Blomberg

Yulong Feng, Lingyi Hao

The vital characteristic of randomness is unpredictability. Thus any regularity will compromise the application of random numbers. Quantum random number generators (QRNGs) can provide intrinsic unpredictable randomness based on the nature of quantum physics, while pseudo-random number generator can not due to the origination of deterministic algorithms or physical processes. However, commonly used traditional test suits are rigorously to test the statistical properties, and the unpredictability of random numbers is still difficult to test. To verify which sources of random numbers are truly unpredictable, in this paper, we propose a new randomness testing method with the artificial neural network (ANN). Random number sequences generated by four different kinds of sources are tested, which are the natural number λ, the linear congruence generator (LCG) pseudo-random algorithm, the Mersenne Twister (MT) pseudorandom algorithm and the QRNG based on vacuum noise, respectively. The testing results indicate that the random sequences from natural number λ and LCG fail to pass our randomness test, while the other two kinds of sequences pass the test successfully due to the relatively simple structure of our ANN. As the complexity of the ANN and the amount of computing power involved increasing, this test method has potential to predict the MT random numbers, and it is also expected that the quantum random numbers can not pass the test with unpredictability no matter how complex the ANN is.

Gregg S. Jaeger

Quantum mechanics is a physical theory supplying probabilities corresponding to expectation values for measurement outcomes. Indeed, its formalism can be constructed with measurement as a fundamental process, as was done by Schwinger, provided that individual measurements outcomes occur in a random way. The randomness appearing in quantum mechanics, as with other forms of randomness, has often been considered equivalent to a form of indeterminism. Here, it is argued that quantum randomness should instead be understood as a form of unpredictability because, amongst other things, indeterminism is not a necessary condition for randomness. For concreteness, an explication of the randomness of quantum mechanics as the unpredictability of quantum measurement outcomes is provided. Finally, it is shown how this view can be combined with the recently introduced view that the very appearance of individual quantum measurement outcomes can be grounded in the Plenitude principle of Leibniz, a principle variants of which have been utilized in physics by Dirac and Gell‐Mann in relation to the fundamental processes. This move provides further support to Schwinger's “symbolic” derivation of quantum mechanics from measurement.

Deborah J. Bennett, Stephen G. Gasiorowicz