  The certification of quantum resources is a critical tool in the development
of quantum information processing. In particular, quantum state verification is
a fundamental building block for communication and computation applications,
determining whether the involved parties can trust the resources at hand or
whether the application should be aborted. Self-testing methods have been used
to tackle such verification tasks in a device-independent (DI) setting.
However, these approaches commonly consider the limit of large (asymptotic),
identically and independently distributed (IID) samples, which weakens the DI
claim and poses serious challenges to their experimental implementation. Here
we overcome these challenges by adopting a theoretical protocol enabling the
certification of quantum states in the few-copies and non-IID regime and by
leveraging a high-fidelity multipartite entangled photon source. This allows us
to show the efficient and device-independent certification of a single copy of
a four-qubit GHZ state that can readily be used for the robust and reliable
implementation of quantum information tasks.
