Coherence scaling in quantum communication protocols

We investigate how quantum coherence scales and is redistributed in quantum communication protocols, using superdense coding and quantum teleportation as paradigmatic case studies. Employing the relative entropy of coherence as a stage-resolved, circuit-level resource measure, we show that multipartite resource states relevant to generalized superdense coding can enable scalable communication while exhibiting only logarithmic or even constant coherence growth, depending on their entanglement structure. In contrast, within the standard teleportation circuit and with coherence evaluated in the computational basis, teleportation displays a protocol-induced coherence contribution that grows linearly with the number of teleported qubits. Through a stage-resolved analysis, we separate coherence generated by the teleportation circuit from message-dependent contributions and identify, at the maximal-coherence pre-measurement stage, a two-bit coherence offset per teleported qubit for computational-basis incoherent inputs, with an additional term given by the input-message coherence in the general case. We further show explicitly that this extensive intermediate coherence generation is fully consistent with information-theoretic bounds, including the Holevo limit, and does not correspond to an increase in accessible classical information.