Table 2 Random numbers from QRNG sources pass the NIST randomness tests.

Statistical test	Single-photon		Phase-noise		Photon-counting		Vacuum-noise		XOR
	P-VAL	Prop.	P-VAL	Prop.	P-VAL	Prop.	P-VAL	Prop.	P-VAL	Prop.
Frequency	0.445	0.989	0.204	0.990	0.846	0.987	0.508	0.993	0.274	0.993
Block Frequency	0.581	0.986	0.406	0.992	0.465	0.994	0.375	0.988	0.871	0.990
Cumulative Sum	0.591	0.987	0.662	0.991	0.591	0.987	0.547	0.994	0.210	0.993
Runs	0.626	0.986	0.239	0.987	0.443	0.991	0.469	0.988	0.793	0.990
Longest Run	0.732	0.982	0.105	0.985	0.437	0.990	0.950	0.987	0.248	0.993
Rank	0.951	0.991	0.102	0.992	0.477	0.987	0.150	0.982	0.720	0.997
FFT	0.170	0.987	0.552	0.990	0.448	0.985	0.017	0.986	0.972	0.987
Non Overlapping	0.121	0.989	0.748	0.990	0.121	0.989	0.143	0.990	0.501	0.990
Overlapping Template	0.233	0.987	0.192	0.992	0.730	0.983	0.022	0.990	0.679	0.986
Universal	0.526	0.989	0.076	0.982	0.538	0.986	0.062	0.990	0.756	0.990
Approximate Entropy	0.820	0.991	0.098	0.990	0.380	0.987	0.625	0.987	0.265	0.995
RandomExcursions (RE)	0.975	0.987	0.980	0.986	0.975	0.987	0.846	0.990	0.100	0.988
RE Variant	0.585	0.987	0.548	0.991	0.585	0.987	0.530	0.990	0.532	0.991
Serial	0.584	0.989	0.050	0.988	0.584	0.989	0.269	0.995	0.722	0.989
Linear Complexity	0.028	0.995	0.115	0.984	0.023	0.990	0.827	0.990	0.087	0.993

For tests with multiple outcomes, a Kolmogorov–Smirnov (KS) uniformity test has been performed for p values (P-VAL), and the corresponding proportions (Prop.) are averaged.

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