Abstract We reverse-engineer, test and analyse hardware firmware of the commercial quantum-optical random number generator Quantis from ID Quantique. show that $>99\%$ > 99 % its output data originates in physically processes: timing photon absorption a semiconductor ma...

The randomness expansion capabilities of semi-device-independent (SDI) prepare and measure protocols are analyzed under the sole assumption that Hilbert state dimension is known. It explicitly proved maximum certifiable entropy can be obtained through this set $\ensuremath{-}{log}_{2}[\frac{1}{2}(1+\frac{1}{\sqrt{3}})]$ same independent witnesses used to certify protocol. minimum number prepara...

Let Qn be the n-dimensional Hamming cube and N = 2n. We prove that number of maximal independent sets in is asymptotically $$2n{2^{N/4}},$$ as was conjectured by Ilinca first author connection with a question Duffus, Frankl Rödl. The value natural lower bound derived from between induced matchings. proof it also an upper draws on various tools, among them “stability” results for set counts old ...