Magic for Hybrid Boson-Fermion Systems: A Grassmann Phase-Space Approach
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908521422913536 |
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| author | Sarkis, Matthieu Martinez-Azcona, Pablo Tkatchenko, Alexandre |
| author_facet | Sarkis, Matthieu Martinez-Azcona, Pablo Tkatchenko, Alexandre |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_05264 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Magic for Hybrid Boson-Fermion Systems: A Grassmann Phase-Space Approach Sarkis, Matthieu Martinez-Azcona, Pablo Tkatchenko, Alexandre Quantum Physics High Energy Physics - Theory 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. |
| title | Magic for Hybrid Boson-Fermion Systems: A Grassmann Phase-Space Approach |
| topic | Quantum Physics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2509.05264 |