Extended Data Fig. 2: NIST tests of randomness.
From: Resolution of 100 photons and quantum generation of unbiased random numbers
Randomness tests for the resultant bit strings based on how the measured data is binned (Mod 8 data shown in the main text). Mod 2, Mod 4, and Mod 8 tests all indicate randomness, while some tests begin to fail for Mod 16 and Mod 32. This is expected due to the non-zero residual biases for a coherent state distribution with mean photon number \(\bar{n}=57\) and a PNRD limit of 100 photons. The error bars for each proportion are computed from the Wilson score (confidence) interval of equation (26) where \(n=\left\{143,287,575,719\right\}\) is the total number of trials for mod\(\left\{2,4,16,32\right\}\) binning, respectively, and \({n}_{s}\,\left({n}_{f}\right)\) are the number of successful (failed) trials for a significance level of α = 0.01. Given repeated testing of the bit generation method, the error bars denote the range for which the proportion is likely to fall. On the horizontal axis, CuSum (F) and (B) denote the cumulative sum tests for forward and backward propagation through the bit sequence, DFT denotes the discrete Fourier transform (spectral) test and Lin. Complex denotes the linear complexity test.
