Amplifying, generating, or certifying randomness

A system for generating a random bit string, the system comprising:

• a weak source of randomness configured to repeatedly generate a first bit string and a second bit string, the first bit string and the second bit string generated in one instance not necessarily having the same values as the first bit string and the second bit string generated in another instance;
• a quantum apparatus configured to receive one or more of the second bit strings and to output an associated third bit string, wherein the quantum apparatus comprises a plurality of quantum systems;
• a security test logic system configured to perform:
• a first security test configured to compute a test statistic, for each of such one or more of the second bit strings the quantum apparatus receives, using the second bit string and the associated third bit string;
• and
• a second security test configured to:
• select a plurality of measurement settings;
• perform a plurality of measurements using the plurality of selected measurement settings;
• generate baseline histograms from the plurality of measurements;
• generate test histograms from the plurality of measurements;
• and
• determine that the plurality of quantum systems are approximately non-signaling based at least in part on a comparison between the baseline histograms and the test histograms;
• wherein the security test logic system is further configured to determine whether to accept or reject the associated third bit string based at least in part on the first security test and the second security test;
• and
• a two-source extractor configured:
• to receive, if the security test logic system accepts the associated third bit string, a bit string based on one or more of the first bit strings and a bit string based on one or more of the third bit strings;
• and
• to generate the random bit string.