No-cloning and no-broadcasting of arbitrary quantum states are intrinsic features differentiating quantum mechanics from the classical realm. Recent studies have explored the broadcasting of quantum features such as asymmetry, magic, and imaginarity within the framework of resource theories. In this work, we study the quantitative aspects of coherence from the perspective of no-broadcasting. Although when the coherence is quantified by a superadditive measure, it can be readily proved that the amount of coherence cannot be broadcast, such an approach becomes invalid for nonsuperadditive measures of coherence. Thus, it is desirable to find methods to study the no-broadcasting of coherence effective for both superadditive and nonsuperadditive coherence measures. By employing a novel characterization of bipartite quantum states with vanishing basis-dependent correlations, we establish a no-broadcasting theorem of coherence in terms of Wigner-Yanase skew information, which is an important version of quantum Fisher information and a nonsuperadditive measure of coherence. The result extends the conventional no-broadcasting from quantum states to information-theoretic contents of quantum states and can be regarded as an instance of no-broadcasting of quantum Fisher information. We also establish no-broadcasting of the relative entropy of coherence, without relying on superadditivity.

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• Quantum coherence & coherence measures
• Quantum foundations
• Quantum information theory