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[GR16]. In the case of quantum communication, we demonstrate that the common randomness rate can be increased by using superdense coding on quantum isotropic states. We also prove an upper bound on the optimal common randomness rate achievable by using one-way quantum communication. As an application, our result yields upper bounds on the classical capacity of the noiseless quantum channel assisted by noisy entanglement[HHH+01].

翻译：本文研究了利用无限量噪声EPR对或量子各向同性态生成最小熵为k的公共随机字符串的问题，且限定爱丽丝与鲍勃之间采用最小通信量。论文考虑了两种通信模型——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，量子各向同性态相对噪声经典关联[GR16]并无优势；而在量子通信情形下，通过在各向同性态上应用超密编码可提升公共随机数速率。此外，我们还证明了采用单向量子通信所能达到的最优公共随机数速率的上界。作为应用，该结果给出了噪声纠缠辅助下无噪声量子信道经典容量[HHH+01]的上界。