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Quantum entanglement and coherence are two fundamental features of nature, arising from the superposition principle of quantum mechanics. While considered as puzzling phenomena in the early days of quantum theory, it is only very recently that entanglement and coherence have been recognized as resources for the emerging
quantum technologies, including quantum Metrology, quantum communication, and quantum computing. In this work we study the limitations for the interconversion between coherence and entanglement. We prove a fundamental no-go theorem, stating that a general resource theory of superposition does not allow for
entanglement activation. By constructing a quantum controlled- NOT gate as a free operation, we experimentally show that such activation is possible within the more constrained framework of quantum coherence. By using recent results from coherence theory, we further show that the trace norm entanglement is not a strong entanglement monotone.