Random number generation by coherent detection of quantum phase noise

In 2010 Qi et al. [Opt. Lett. 35(3), 312 (2010)] demonstrated a random number generator based on the drift of the phase of a laser due to spontaneous emission, The out-of-the-lab implementation of this scheme presents two main drawbacks: it requires a long and highly unbalanced interferometer to generate a random phase with uniform probability distribution, or alternatively, a shorter and slightly unbalanced interferometer that notwithstanding requires active stabilization and does not generate a uniform probability distribution without randomness extraction. Here we demonstrate that making use of the random nature of the phase difference between two independent laser sources and two coherent detectors we can overcome these limitations. The two main advantages of the system demonstrated are: i) it generates a probability distribution of quantum origin which is intrinsically uniform and thus in principle needs no randomness extraction for obtaining a uniform distribution, and ii) the phase is measured with telecom equipment routinely used for high capacity coherent optical communications. The speed of random bit generation is determined by the photodetector bandwidth and the linewidth of the lasers. As a by-product of our method, we have obtained images of how phase noise develops with time in a laser. This provides a highly visual alternative way of measuring the coherence time of a laser.