  We experimentally demonstrate that it is impossible to simulate quantum
bipartite correlations with a deterministic universal Turing machine. Our
approach is based on the Normalized Information Distance (NID) that allows the
comparison of two pieces of data without detailed knowledge about their origin.
Using NID, we derive an inequality for output of two local deterministic
universal Turing machines with correlated inputs. This inequality is violated
by correlations generated by a maximally entangled polarization state of two
photons. The violation is shown using a freely available lossless compression
program. The presented technique may allow to complement the common statistical
interpretation of quantum physics by an algorithmic one.
