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Quantum Algebras Associated With Bell States
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.Comment: v1: 15 pages, 2 figures, latex; v2: 18 pages, 2 figures, latex,
references and notes adde