Non-Local and Quantum Advantages in Network Coding for Multiple Access Channels

Abstract: Devising efficient communication in a network consisting of multiple transmitters and receivers is a problem of immense importance in communication theory. Interestingly, resources in the quantum world have been shown to be very effective in enhancing the performance of communication networks. In this work, we study entanglement-assisted communication over classical network channels. When there is asymmetry such that noise introduced by the channel depends on the input alphabets, non communicating senders may exploit shared entangled states to overcome the noise. We consider multiple access channels, an essential building block for many complex networks, and develop an extensive framework for n-senders and 1-receiver multiple access channels based on nonlocal games. We obtain generic results for computing correlation assisted sum-capacities of these channels. The considered channels introduce less noise on winning and more noise on losing the game, and the correlation assistance is classified as local (L), quantum (Q), or no-signaling (NS). Furthermore, we consider a broad class of multiple access channels such as depolarizing ones that admix a uniform noise with some probability and prove general results on their sum-capacities. Finally, we apply our analysis to three specific depolarizing multiple access channels based on Clauser-Horne-Shimony-Holt, magic square, and Mermin-GHZ nonlocal games. In all three cases we find significant enhancements in sum-capacities on using nonlocal correlations. We obtain either exact expressions for sum-capacities or suitable upper and lower bounds on them. The general framework developed in this work has much wider applicability and the specificity studied in details are some illustrative examples to compare with recent studies in this direction.