This paper addresses the problem of generating a common random string with min-entropy k using an unlimited supply of noisy EPR pairs or quantum isotropic states, with minimal communication between Alice and Bob. The paper considers two communication models -- one-way classical communication and one-way quantum communication, and derives upper bounds on the optimal common randomness rate for both models. We show that in the case of classical communication, quantum isotropic states have no advantage over noisy classical correlation, and that the optimal common randomness rate can be achieved by a classical strategy, in which Alice and Bob share classical $\rho$-correlated random variables. In the case of quantum communication, we demonstrate that the common randomness rate can be increased by using superdense coding on quantum isotropic states. Our main result is an upper bound on the optimal common randomness rate achievable by using one-way quantum communication. We also provide an application of this result, which yields upper bounds on the classical capacity of the noiseless quantum channel assisted by noisy entanglement.

翻译：本文研究在Alice和Bob之间通信量最小的情况下，利用无穷多含噪EPR对或量子各向同性态生成最小熵为k的公共随机串问题。论文考虑两种通信模型——单向经典通信与单向量子通信，并推导了两种模型下最优公共随机数速率的上界。我们证明：在经典通信情形下，量子各向同性态相比于含噪经典关联并无优势，且可通过经典策略实现最优公共随机数速率——此时Alice与Bob共享经典ρ关联随机变量。在量子通信情形下，我们证实对量子各向同性态采用超密编码可提升公共随机数速率。主要成果是给出了通过单向量子通信可达的最优公共随机数速率上界。此外，我们提供了该结果的一个应用，它推导出由含噪纠缠辅助的无噪量子信道经典容量上界。