A Phase-Space Geometric Measure of Magic in Qubit Systems

Quantum Physics [Submitted on 21 Mar 2026] A Phase-Space Geometric Measure of Magic in Qubit Systems Soumyojyoti Dutta, Tushar Characterizing quantum magic -- the resource enabling computational advantage beyond stabilizer circuits -- is subtle in qubit systems because established measures can give conflicting information about the same state. We introduce C(rho), the l1 distance from a state's discrete Wigner function to the convex hull of stabilizer Wigner functions, and study its relationship to the stabilizer extent Gamma(rho) via the tightness ratio kappa(rho) := (Gamma(rho)-1)/C(rho). For three two-qubit families in the repetition-code subspace span{|00>,|11>}, we prove kappa takes exact integer values constant over each family: kappa=1 for the R_y and Bell+R_z families, kappa=2 for the R_x family. The factor-of-2 gap arises because imaginary coherence concentrates Wigner negativity at 2 of 16 phase-space points rather than 4, leaving Gamma unchanged. The optimal dual witnesses are logical Pauli operators of the repetition code, revealing that C is a fault-tolerant observable invariant under correctable errors -- an unexpected connection between phase-space geometry and quantum error correction. We prove a sharp bound Gamma >= 1 + C/M_n, establish a hemispheric dichotomy in tensor-product behavior where superadditivity of C fails for northern-hemisphere states with deficit approximately 0.335 C(rho), and show C is not a magic monotone under the full Clifford group, so asymptotic distillation rates require Gamma. Comments: 19 pages, 7 figures Subjects: Quantum Physics (quant-ph) MSC classes: 81P68, 81P45, 81P16 Cite as: arXiv:2603.20792 [quant-ph]   (or arXiv:2603.20792v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2603.20792 Focus to learn more Submission history From: Soumyojyoti Dutta [view email] [v1] Sat, 21 Mar 2026 12:33:13 UTC (1,469 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-03 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)