Measurement-device-independent randomness from local entangled states

Nonlocal correlations are useful for device independent (DI) randomness certification [Nature (London) {\bf 464}, 1021 (2010)]. The advantage of this DI protocol over the conventional quantum protocol is that randomness can be certified even when experimental apparatuses are not trusted. Quantum entanglement is the necessary physical source for the nonlocal correlation required for such DI task. However, nonlocality and entanglement are distinct concepts. There exist entangled states which produce no nonlocal correlation and hence are not useful for the DI randomness certification task. Here we introduce the measurement-device-independent randomness certification task where one has trusted quantum state preparation device but the measurement devices are completely unspecified. Interestingly we show that there exist entangled states, with local description, that are useful resource in such task which otherwise are useless in corresponding DI scenario.