  Non-classical correlations arising in complex quantum networks are attracting
growing interest, both from a fundamental perspective and for potential
applications in information processing. In particular, in an entanglement
swapping scenario a new kind of correlations arise, the so-called nonbilocal
correlations that are incompatible with local realism augmented with the
assumption that the sources of states used in the experiment are independent.
In practice, however, bilocality tests impose strict constraints on the
experimental setup and in particular to presence of shared reference frames
between the parties. Here, we experimentally address this point showing that
false positive nonbilocal quantum correlations can be observed even though the
sources of states are independent. To overcome this problem, we propose and
demonstrate a new scheme for the violation of bilocality that does not require
shared reference frames and thus constitute an important building block for
future investigations of quantum correlations in complex networks.
