Fast quantum-optical random-number generators

In this paper we study experimentally the properties of three types of quantum -optical random-number generators and characterize them using the available National Institute for Standards and Technology statistical tests, as well as four alternate tests. The generators are characterized by a trade-off between, on one hand, the rate of generation of random bits and, on the other hand, the degree of randomness of the series which they deliver. We describe various techniques aimed at maximizing this rate without diminishing the quality (degree of randomness) of the series generated by it.

Figure 1

The variance of the measured laser intensity (circles) is directly proportional to the average value of the laser current according to Eq. (2) (straight line).

Figure 2

Photo of our setup, which is based on the Quantis QRNG.

Figure 3

Experimental [filled (blue) circles] and theoretical [solid (red) lines] histogram of time delay between clicks in photon detector 1 at (a) high intensity and (b) low intensity.

Figure 4

Law of large numbers [vertical (black) line] and SeQuR QRNG: raw data for the bit1[open (blue) circles and solid (blue) line] and bit3 [(red) X's and dashed (red) line] series. The bit1 series reveals a substantial irregularity of the standard deviation, while the bit3 series behaves as would be expected for a random bit series. This is also confirmed by the example $p$ values calculated for both series.

Figure 5

Autocorrelation plot for SeQuR QRNG raw data: the bit1 series [open (blue) circles and solid (blue) line] reveals a strong correspondence within the random sequence, while the bit3 series [(red) X's and dashed (red) line] behaves as would be expected for a random bit series. This is confirmed by the $p$ values.

Figure 6

Same as Fig. 4, but for SeQuR QRNG filtered data: the bit1 sequence exhibits a departure from ideal randomness for data samples smaller than 300, while the bit3 series behaves as would be expected for a random bit series. The respective $p$ values confirm this result.

Figure 7

Same as Fig. 5, but for SeQuR QRNG filtered data: the autocorrelation plot for the bit1 sequence shows strong correlations, of order 10, while the bit3 series behaves as would be expected for a random bit series. The $p$ values show that the bit 3 sequence passes the test for an interval length of ${10}^3$.

Figure 8

Autocorrelation in the random file generated using the split method, in the “slow” and ”fast” regimes, e.g., strongly and less strongly attenuated light, with $\tau =300$ ns and $\tau =190$ ns, respectively: solid (blue) line with open (blue) circles and dashed (red) line with (red) X's, respectively.

Figure 9

Autocorrelation in the random file generated using the split method, in the “slow”regime and after applying the Von Neumann extractor [solid (blue) line with open (blue) circles], the Von Neumann extractor and then xor [dashed (red) line with (red) X's], and xor and then the Von Neumann extractor [dotted (green) line with filled (green) circles].

Figure 10

Autocorrelation in the random file generated using the parity method, in the “slow” and ”fast” regimes: dashed (red) curve and solid (blue) curves, respectively.