Randomness-free Test of Non-classicality: a Proof of Concept

Quantum correlations and non-projective measurements underlie a plethora of information-theoretic tasks, otherwise impossible in the classical world. Existing schemes to certify such non-classical resources in a device-independent manner require seed randomness -- which is often costly and vulnerable to loopholes -- for choosing the local measurements performed on different parts of a multipartite quantum system. In this letter, we propose and experimentally implement a semi-device independent certification technique for both quantum correlations and non-projective measurements without seed randomness. Our test is {\it semi-device independent} in the sense that it requires only prior knowledge of the dimension of the parts. By producing specific correlated coins from pairs of photons entangled in their transverse spatial modes we experimentally show a novel quantum advantage in correlated coin tossing. We establish the advantage by showing that the correlated coin procured from the entangled photons cannot be obtained from any two 2-level classical correlated coins. The quantum advantage requires performing qubit trine positive operator-valued measures (POVMs) on each part of the entangled pair, thus also certifying such POVMs in a semi-device-independent manner. This proof of concept firmly establishes a new cost-effective certification technique for both, generating non-classical shared randomness and implementing non-classical measurements which will be important for future multi-party quantum communications.