Toward an improved understanding of the role of quantum information in nuclei and exotic matter, we examine the magic (non-stabilizerness) in low-energy strong interaction processes. As stabilizer states can be prepared efficiently using classical computers, and include classes of entangled states, it is magic and fluctuations in magic, along with entanglement, that determine resource requirements for quantum simulations. As a measure of fluctuations in magic induced by scattering, the “magic power” of the S-matrix is introduced. Using experimentally determined scattering phase shifts and mixing parameters, the magic power in nucleon-nucleon and hyperon-nucleon scattering, along with the magic in the deuteron, are found to exhibit interesting features. The Sigma-minus baryon is identified as a potential candidate catalyst for enhanced spreading of magic and entanglement in dense matter, depending on in-medium decoherence.