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，一对分布式代理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$(U_d,V_d)$，其联合分布$P_{U_d,V_d}$在总变差距离下收敛于目标分布$Q_{U,V}$。考虑标准NISS场景的两种变体：第一种变体中，除$(X^d,Y^d)$外，代理还可访问共享贝尔态。代理各自测量其状态（测量方式自选），并将测量经典输出与$(X^d,Y^d)$结合以模拟目标分布，该场景称为纠缠辅助NISS（EA-NISS）。第二种变体中，除$(X^d,Y^d)$外，代理还可访问经典公共随机比特$Z$，该场景称为经典公共随机性NISS（CR-NISS）。研究表明，对于二元输出的NISS场景，EA-NISS与CR-NISS的可行分布集合相等，故此类EA-NISS场景中不存在量子优势。对于非二元输出的NISS场景，通过实例证明存在EA-NISS可行而CR-NISS不可行的分布，这表明在非二元输出EA-NISS中具有量子优势。