Postprocessing for quantum random-number generators: Entropy evaluation and randomness extraction

Quantum random-number generators (QRNGs) can offer a means to generate information-theoretically provable random numbers, in principle. In practice, unfortunately, the quantum randomness is inevitably mixed with classical randomness due to classical noises. To distill this quantum randomness, one needs to quantify the randomness of the source and apply a randomness extractor. Here, we propose a generic framework for evaluating quantum randomness of real-life QRNGs by min-entropy, and apply it to two different existing quantum random-number systems in the literature. Moreover, we provide a guideline of QRNG data postprocessing for which we implement two information-theoretically provable randomness extractors: Toeplitz-hashing extractor and Trevisan's extractor.

Figure 1

A generic schematic diagram of a QRNG setup. A quantum state is prepared and measured. Then the outcome is processed to generate random numbers by an extractor.

Figure 2

Autocorrelation evaluation results. All normalized correlation is evaluated from a 10 Mb record of the raw data. (a) Autocorrelation of the raw data (between bits). The average value of autocorrelation coefficient is $9.5\times {10}^{-4}$. The most significant correlations are within eight bits, due to the usage of eight-bit ADC. (b) Autocorrelation of the raw data (between samples). The average value is $4.9\times {10}^{-4}$. (c) Autocorrelation of the outcomes from the Toeplitz-hashing extractor. The average value is $-1.0\times {10}^{-5}$. (d) Autocorrelation of the outcomes from Trevisan's extractor. The average value is $1.6\times {10}^{-5}$. In theory, for a truly random $10\times {10}^6$ bit string, the average normalized correlation coefficient is 0 with a standard deviation of $4\times {10}^{-4}$.