The illusionist game and hidden correlations

We suggest and demonstrate a new protocol based on correlated beams of light: the 'optical illusionist game'. An 'illusionist' at first shows that if two uncorrelated light beams excited in the same Gaussian state are mixed in a beam splitter, then no correlations arise between them, as it was not present. On the other hand, when correlations with an ancillary state are exploited, the presence of the beam splitter can be unveiled. (paper)