  Quantum nonlocality stands as a resource for Device Independent Quantum
Information Processing (DIQIP), as, for instance, Device Independent Quantum
Key Distribution. We investigate experimentally the assumption of limited
Measurement Dependence, i.e., that the measurement settings used in Bell
inequality tests or DIQIP are partially influenced by the source of entangled
particle and/or by an adversary. Using a recently derived Bell-like inequality
[Phys. Rev. Lett. 113 190402] and a 99% fidelity source of partially entangled
polarization photonic qubits, we obtain a clear violation of the inequality,
excluding a much larger range of measurement dependent local models than would
be possible with an adapted Clauser, Horne, Shimony and Holt (CHSH) inequality.
It is therefore shown that the Measurement Independence assumption can be
widely relaxed while still demonstrating quantum nonlocality.
