Abstract

We demonstrate that with a pair of deterministic universal Turing machines (Fig. 1), it is impossible to replicate the observed quantum bipartite correlations from a spontaneous parametric down-conversion (SPDC) experiment. Using the concept of Kolmogorov complexity K [1] and a Normalised Compression Distance (NCD) [2] which allows for a comparison of two pieces of data without detailed knowledge about their characteristics, we derive an inequality [2] S(A,B) = NCD(A0, B1) − NCD(A0, B0) − NCD(A1, B0) − NCD(A1, B1) ≤ 0, that must be obeyed by data generated by two local deterministic universal Turing machines with correlated inputs. With the correlations generated by a maximally entangled polarisation state of two photons, we experimentally probe the dependence of S on the experimental settings (Fig. 2). With the accumulated statistics from repeated measurements at the optimsed setting, we violate this inequality with a value of S = 0.151 ± 0.007, more than 21 standard deviation above the classical limit. The evaluation of the inequality is done by estimating K with conventional lossless compression programs [3] which are routinely used on common computing platforms. We also briefly discuss philosophical and information-theoretical implications of our results.

© 2015 IEEE