Experimental evidence of quantum randomness incomputability

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—an asymptotic property—of quantum randomness by performing finite tests of randomness inspired by algorithmic information theory.

Figure 1

Box-and-whisker plot for the results of the “book stack” randomness test.

Figure 2

Box-and-whisker plot for the results based on the Solovay-Strassen probabilistic primality test.

Figure 3

Box-and-whisker plot for the results for tests of the Borel normality property.

Figure 4

Box-and-whisker plot for average results in “sliding window” estimations of the Shannon entropy.

Figure 5

Box-and-whisker plot for the results of the random walk tests.