Randomness of imperfectly entangled states

TL;DR

This study compares the randomness of series generated from biphotons with varying entanglement levels, finding that less entanglement correlates with higher randomness, relevant for quantum key distribution.

Contribution

It provides an empirical analysis of how different levels of entanglement affect the quality of generated random series, independent of non-locality considerations.

Findings

No entangled states produce the most random series.

Marginally entangled states yield the least random series.

Entangled states are still acceptable for quantum key distribution.

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.