Magic Entropy in Hybrid Spin-Boson Systems

We introduce entropic measures to quantify non-classical resource in hybrid spin-boson systems. We discuss the stabilizer R´enyi entropy in the framework of phase space quantisation and define an analogous hybrid magic entropy and a mutual magic entropy that capture the distribution of quantum magic across spin and bosonic subsystems. We use these entropic measures to demonstrate two key phenomena: the detection of the superradiant phase transition in the Dicke model and the dynamics of magic in the Jaynes-Cummings model following a quench. We develop a Monte Carlo numerical scheme to enable practical computation in many-body examples.