Abstract
This work considers the non-interactive source simulation problem (NISS). In the standard NISS scenario, a pair of distributed agents, Alice and Bob, observe a distributed binary memoryless source (X^d,Y^d) generated based on joint distribution P_X,Y. The agents wish to produce a pair of discrete random variables (U_d,V_d) with joint distribution P_U_d,V_d, such that P_U_d,V_d converges in total variation distance to a target distribution Q_U,V. Two variations of the standard NISS scenario are considered. In the first variation, in addition to (X^d,Y^d) the agents have access to a shared Bell state. The agents each measure their respective state, using a measurement of their choice, and use its classical output along with (X^d,Y^d) to simulate the target distribution. This scenario is called the entanglement-assisted NISS (EA-NISS). In the second variation, the agents have access to a classical common random bit Z, in addition to (X^d,Y^d). This scenario is called the classical common randomness NISS (CR-NISS). It is shown that for binary-output NISS scenarios, the set of feasible distributions for EA-NISS and CR-NISS are equal with each other. Hence, there is not quantum advantage in these EA-NISS scenarios. For non-binary output NISS scenarios, it is shown through an example that there are distributions that are feasible in EA-NISS but not in CR-NISS. This shows that there is a quantum advantage in non-binary output EA-NISS.