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

• URL: http://arxiv.org/abs/2509.05264v1
• Date: Fri, 05 Sep 2025 17:22:54 GMT
• Title: Magic for Hybrid Boson-Fermion Systems: A Grassmann Phase-Space Approach
• Authors: Matthieu Sarkis, Pablo Martinez-Azcona, Alexandre Tkatchenko,
• Abstract summary: Non-stabilizerness enables universality beyond Gaussian/Clifford dynamics.<n>No resource theory exists for systems combining bosonic and fermionic modes.<n>We develop a phase-space framework defining hybrid magic via the $L_p$ norm of a hybrid Wigner function.
• Score: 42.13843953705695
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Non-stabilizerness enables universality beyond Gaussian/Clifford dynamics, yet no resource theory exists for systems combining bosonic and fermionic modes. 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.

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