Randomness of imperfectly entangled states

Abstract

The generation of series of random numbers is an important and difficult problem. Appropriate measurements on entangled states have been proposed as the definitive solution, based on the impossibility of exploiting quantum non locality to get faster than light signaling. There is a controversy regarding what is preferable to produce series with utilizable randomness in practice, high or low entanglement. We prepare biphotons with three different levels of entanglement, easy entangled, marginally entangled and no entangled. Randomness is evaluated, independently of the quantum non locality argument, through a battery of standard statistical tests, Hurst exponent, Kolmogorov complexity, Takens dimension of embedding, and Augmented Dickey Fuller and Kwiatkowski Phillips Schmidt Shin tests to check stationarity. The no entangled case is found to produce the smallest rate of not random series, and the marginal case the largest. Although the entangled case has a larger rate of not random series than the no entangled case, it is found still acceptable for QKD.