  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].
