Researchers have quantified the advantage of quantum communication over classical communication in star-network topologies. They designed an exclusion task that can be perfectly solved using quantum $d$-level systems (qudits), whereas a classical solution would require a large message. This work establishes a lower bound on the classical simulation cost of certain quantum correlations, highlighting that quantum communication can significantly outperform classical communication in specific scenarios.

The study focuses on a scenario where multiple parties each send a quantum system to a central node for a joint measurement. The proposed exclusion task cannot be solved with certainty if each of the $n$ parties sends a classical message with fewer than $n^{(d-1)}$ symbols. This result implies an exponential advantage for quantum messages, scaling with both the dimension of the quantum system ($d$) and the number of simultaneously measured systems ($n$).

This finding has significant implications for understanding quantum correlations and communication complexity. For instance, it shows that no finite-size classical description of a qubit suffices to reproduce the statistics of a joint measurement on sufficiently many qubits. This underscores the intrinsically non-classical nature of certain quantum properties and their potential to surpass classical information processing capabilities.