Complexity of quantum states in the stabilizer formalism

Quantum Physics [Submitted on 22 Apr 2026] Complexity of quantum states in the stabilizer formalism Shuangshuang Fu, Shunlong Luo, Yue Zhang We initiate an investigation into a notion of state complexity for discrete-variable quantum systems. Specifically, we propose an information-theoretic quantifier for the complexity of quantum states within the stabilizer formalism of quantum computation. This is achieved by leveraging the symmetric Jordan product (associated with classicality) and the skew-symmetric Lie product (linked to quantumness) between the square root of the quantum state and the Heisenberg-Weyl displacement operators. We establish the fundamental properties of this quantifier and demonstrate that state complexity is closely related to the nonstabilizerness of quantum states via the L^4-norm of their characteristic functions. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2604.20118 [quant-ph]   (or arXiv:2604.20118v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.20118 Focus to learn more Submission history From: Yue Zhang [view email] [v1] Wed, 22 Apr 2026 02:29:12 UTC (14 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 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?)