2006/10/31 by Yong Zhang, Naihuan Jing, Mo-Lin Ge
Computer Science · Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebra over a field #Algebraic structure #Algebraic structures and combinatorial models #Antisymmetric relation #Bell polynomials #Bell state #Categorical quantum mechanics #Coproduct #Product (mathematics) #Quantum #Quantum Information and Cryptography #Quantum affine algebra #hep-th #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1088/1751-8113/41/5/055310
published as J. Phys. A: Math. Theor. 41 (2008) 055310 · v1: 15 pages, 2 figures, latex; v2: 18 pages, 2 figures, latex, references and notes added
arxiv created 2006/11/06 · openalex publication_date 2008/01/23 · arxiv updated 2015/06/26 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The antisymmetric solution of the braided Yang--Baxter equation called the Bell matrix becomes interesting in quantum information theory because it can generate all Bell states from product states. In this paper, we study the quantum algebra through the FRT construction of the Bell matrix. In its four dimensional representations via the coproduct of its two dimensional representations, we find algebraic structures including a composition series and a direct sum of its two dimensional representations to characterize this quantum algebra. We also present the quantum algebra using the FRT construction of Yang--Baxterization of the Bell matrix.