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.

翻译：本文研究非交互式源模拟问题（NISS）。在标准NISS场景中，分布式代理Alice和Bob观测到基于联合分布$P_{X,Y}$生成的分布式二元无记忆源$(X^d,Y^d)$。代理希望生成一对离散随机变量$(U_d,V_d)$，使其联合分布$P_{U_d,V_d}$在总变差距离上收敛于目标分布$Q_{U,V}$。研究考虑了标准NISS场景的两种变体：第一种变体中，除$(X^d,Y^d)$外，代理共享一个Bell态。代理各自使用自选测量方式测量其状态，并将测量经典输出与$(X^d,Y^d)$结合以模拟目标分布，该场景被称为纠缠辅助NISS（EA-NISS）；第二种变体中，除$(X^d,Y^d)$外，代理共享经典公共随机比特$Z$，该场景被称为经典公共随机性NISS（CR-NISS）。研究表明，对于二元输出NISS场景，EA-NISS与CR-NISS的可行分布集合完全相等，因此在此类EA-NISS场景中不存在量子优势。而对于非二元输出NISS场景，通过反例证明存在EA-NISS可行但CR-NISS不可行的分布，这表明非二元输出EA-NISS中确实存在量子优势。