Optical Quantum Random Number Generator

A physical random number generator based on the intrinsic randomness of quantum mechanics is described. The random events are realized by the choice of single photons between the two outputs of a beamsplitter. We present a simple device, which minimizes the impact of the photon counters’ noise, dead-time and after pulses. Random numbers are employed today as well for numerical simulations as for cryptography. Unfortunately computers are not able to generate true random numbers, as they are deterministic systems. Numerical pseudo-random generators rely on complexity [1]. Although such pseudo-random numbers can generally be employed for numerical computation, such as MonteCarlo simulations, their use in cryptography, for example to generate keys, is more critical. The only way to get true random numbers, hence true security for crypto-systems, is to build a generator based on a random physical phenomenon [2,3,4]. As quantum theory is intrinsically random, a quantum process is an ideal base for a physical random number generator. The randomness of a sequence of numbers can be extensively tested, though not proven. It is thus of interest to thoroughly understand the behavior of the random process, so as to gain confidence in its proper random operation. A statistical process, however, is generally hard to analyze because it involves a lot of variables. Fortunately, some quantum processes can be well described with only a few variables, like, for example, the random choice of a single photon between the two outputs of a beamsplitter [5,6,7]. In this paper, we present a simple, easy to use and potentially cheap random number generator based on this quantum process and on the technique of single photon counting. It fulfills the two major requirements for a physical random number generator: low correlations between successive outputs and stability to external perturbations. The principle of the generator is illustrated in the figure 1. Weak pulses of a 830 nm LED are coupled into a monomode fibre. At the output of the 2 meter long monomode fibre all photons are in the same mode, therefore indistinguishable, irrespective of any thermal fluctuation of the LED. They then impinge on two multimode fibres glued together some mm away from the monomode fiber. Both multimode fibers are coupled to the same photon counter, one of the multimode fiber introducing a 60 ns delay. By detecting the time of arrival of the photon one can determine which path it took. Labeling the short path by ’0’ and the long by ’1’ one obtain a sequence of random bits. The generation rate is of approximately 100kHz, corresponding to 0.1 photon per pulse as the LED is pulsed at 1MHz. Note that a Poissonnian photon number distribution with mean number 0.1 is a good approximation to the ideal single photon deltadistribution. A FPGA circuit [Xilinx XC 3130] is used to pulse the LED and to detect the coincidences. It features three counters, one for the ’0’ bits, one for the ’1’, defined by two 10 ns large time windows corresponding to the two different arrival times. The third counter