Unified approach for computing sum of sources over CQ-MAC

We consider the task of communicating a generic bivariate function of two classical sources over a Classical-Quantum Multiple Access Channel (CQ-MAC). The two sources are observed at the encoders of the CQ-MAC, and the decoder aims at reconstructing a bivariate function from the received quantum state. Inspired by the techniques developed for the classical setting, and employing the technique of simultaneous (joint) decoding developed for the CQ setup, we propose and analyze a coding scheme based on a classical superposition of algebraic structured codes and unstructured codes, and the idea of embedding functions on a prime field. We derive a new set of sufficient conditions that strictly enlarge the largest known set of sources (capable of communicating the bivariate function) for any given CQ-MAC. We provide these conditions in terms of single-letter quantum information-theoretic quantities.