Stabilizer and Clifford one-way quantum communication protocols are classically simulable with shared randomness, so magic resources are required for quantum advantage in one-way communication complexity.
Kushilevitz, Communication Complexity, in Advances in Computers (Elsevier, 1997) p
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Gottesman-Knill Limit on One-way Communication Complexity: Tracing the Quantum Advantage down to Magic Resources
Stabilizer and Clifford one-way quantum communication protocols are classically simulable with shared randomness, so magic resources are required for quantum advantage in one-way communication complexity.