Randomness-free Test of Non-classicality and An Experimental Quantum Advantage in Correlated Coin Tossing

Quantum entanglement leads to non-classical correlations certifiable through Bell tests. These tests 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. We implement a technique of detecting the non-classicality of correlations that does not require seed randomness. Our test is semi-device-independent and 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 also experimentally show a novel quantum advantage in correlated coin tossing. We establish the advantage by showing that the correlated coin state we obtain cannot be derived from any two 2-level classical correlated coins. The quantum advantage requires performing qubit trine positive operator value measures (POVMs) on each part of the entangled pair, thus also certifying such POVMs in a semi-device-independent manner. We firmly establish a quantum advantage in generating shared randomness which will be important for future multi-party quantum communications.