Nonlocal and quantum advantages in network coding for multiple access channels

In this work, we consider two-sender, one-receiver communication over a discrete memoryless multiple-access channel without feedback, where two senders may cooperate on channel coding by using preshared resources, such as shared randomness, quantum states and measurements, or nonlocal correlations. We present the capacity region when senders employ cooperative encoding with quantum and nonlocal resources, extending beyond shared randomness, and derive a sum rate that serves as a lower bound to the sum capacity; the lower bound is computable by exploiting specific strategies. We also compute the sum capacities for two instances. One is when senders apply local resources for cooperative encoding. The other is when senders exploit nonclassical resources for encoding against channels constructed by referring to nonlocal games; in this way, correlated noise other than independent errors occurs on code words. Comparing the exact sum capacities and lower bounds, we show that nonlocal and quantum resources for cooperative encoding enable higher sum capacities over local ones. The Clauser-Horne-Shimony-Holt and magic square games are considered for constructing multiple-access channels, and we demonstrate the usefulness of nonlocal and quantum resources to achieve higher-sum capacities.