Magic for Hybrid Boson-Fermion Systems: A Grassmann Phase-Space Approach

Abstract:Non-stabilizerness enables universality beyond Gaussian/Clifford dynamics, yet no resource theory exists for systems combining bosonic and fermionic degrees of freedom. Using the Grassmann approach of Cahill and Glauber, we develop a phase-space framework defining hybrid magic via the $L_p$ norm of a hybrid Wigner function. We demonstrate it in the Holstein polaron, where phonon-electron coupling enhances magic growth, and in the fermionic Jaynes-Cummings model, examining dependence on atomic and cavity states. At the gate level, we define the non-stabilizer power of hybrid operations and derive a closed-form result for the conditional displacement gate. This establishes a unified quantification of non-stabilizerness in realistic hybrid systems.

arXiv:2509.05264 [quant-ph]

(or arXiv:2509.05264v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2509.05264 Focus to learn more arXiv-issued DOI via DataCite

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