  Self-testing is a method of quantum state and measurement estimation that
does not rely on assumptions about the inner working of the used devices. Its
experimental realization has been limited to sources producing single quantum
states so far. In this work, we experimentally implement two significant
building blocks of a quantum network involving two independent sources, i.e. a
parallel configuration in which two parties share two copies of a state, and a
tripartite configuration where a central node shares two independent states
with peripheral nodes. Then, by extending previous self-testing techniques we
provide device-independent lower bounds on the fidelity between the generated
states and an ideal state made by the tensor product of two maximally entangled
two-qubit states. Given its scalability and versatility, this technique can
find application in the certification of larger networks of different
topologies, for quantum communication and cryptography tasks and randomness
generation protocols.
