Star product for qubit states in phase space and star exponentials

Quantum Physics [Submitted on 6 Apr 2026] Star product for qubit states in phase space and star exponentials Jasel Berra-Montiel, Alberto Molgado, Mar Sánchez-Córdova In this paper, we formulate the phase space description of qubit systems using coadjoint orbits of SU(2) and the Stratonovich-Weyl correspondence, yielding a deformation quantization on the sphere. The resulting star product reproduces the operator algebra of complexified quaternions and its antisymmetric part induces the Lie-Poisson structure associated with the Kirillov-Kostant-Souriau symplectic form. We show that quantum dynamics can be expressed entirely in phase space through star exponentials of Hamiltonian symbols, leading to an explicit representation of the propagator. Further, we establish the equivalence between the coherent-state path integral formulation on S^2 and the algebraic description in terms of star exponentials. Some examples illustrating the construction of the star-exponential functions and the resulting Poisson structure are included. Comments: 14 pages, no figures Subjects: Quantum Physics (quant-ph); Mathematical Physics (math-ph) MSC classes: 81S30 Cite as: arXiv:2604.05170 [quant-ph]   (or arXiv:2604.05170v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.05170 Focus to learn more Submission history From: Jasel Berra-Montiel [view email] [v1] Mon, 6 Apr 2026 21:00:45 UTC (34 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 Change to browse by: math math-ph math.MP 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?)